Course Co-ordinated by IIT Bombay
 NPTEL >> Courses >> Electronics & Communication Engineering >> Adv. Digital Signal Processing - Multirate and wavelets (Video) >> L1- Introduction
Question in Lecture
 Ask a Question Question Topics : Question:     Max: 300 char

All Questions

 Question: Sir, In what sense wavelet can be used as a feature extractor? By: Sachin Sharma     Date: 2012-01-15 Answer: You must have been, in some of the lectures, that 2-D wavelets provide information on vertical, horizontal and diagonal features of images. In fact, one could verify this by taking the 2-D wavelet transform of an image - particularly an image which has clearly distinguishable vertically significant, horizontally significant and/or diagonally significant features. The 2-D wavelet transform involves a 1-D wavelet transform on each of the dimensions. Beyond horizontal, vertical and diagonal features, one would need to see if a feature manifests itself in one, or more than one, band. A 'feature' could mean a particular edge pattern, or a shape for example. One would then have to look for that manifestation in a test image. This is a preliminary answer. I guess if I understand your specific context better, a more pointed answer can be given. By: Prof. V.M. Gadre     Date: 2012-01-17

 Question: 1.How to draw a Phase plot.For eg when we take fourier transform of rect pulse the magnitude is sinc function but what about phase?2.Is there any relation between magnitude plot and phase plot?When should one add 180 degrees to the phase plot?3.What is the importance of phase in signal processing? By: ManojNiranjan.P     Date: 2012-02-06 Answer: Let us take your last question first. The importance of phase in signal processing is often like a 'necessary evil' - like friction in mechanical systems. Phase is normally required on account of causality. If causality were not required, then one could have real and even Fourier Transforms for real systems (systems with real impulse responses). Thus the phase would be either 0 or 180 degrees. For a real causal system, the magnitude and phase can be related. In fact, one can see this from the fact that for a real causal system, the real and even part of the impulse response can be constructed from the original impulse response, which corresponds to the real component of the spectrum. So too, a similar process can be followed for the imaginary component. If the magnitude of the spectrum is known, the magnitude together with one of these can give information about the phase. By: Prof. V.M. Gadre     Date: 2012-02-10

 Question: Why linear phase is considered important in most of the systems though practically the systems are nonlinear? By: ManojNiranjan.P     Date: 2012-02-06 Answer: 'Linear Phase' or 'Nonlinear phase' is a term which can only be used only with systems which are linear, shift invariant and which admit a frequency response. Linear phase essentially means no dispersion, that is, all sinusoidal components suffer the same time shift and are not RELATIVELY shifted. Nonlinear SYSTEMS cannot strictly be associated with a phase response. By: Prof. V.M. Gadre     Date: 2012-02-10

 Question: Dear Sir, What is the unit of Normalized Digital Angular frequency(small omega)Is it radians or radians/sample? Is there any difference between radians and radians/sample? By: ManojNiranjan.P     Date: 2012-06-07 Answer: Notionally, you could take it to be radians per sample. Remember, 'sample' itself is without units. It is accurate to say that the normalized angular frequency indicates the angle covered in one sample time. The maximum allowable angle that can be covered in one sample time is therefore 'pi' radians, giving exactly two samples per cycle. By: Prof. V.M. Gadre     Date: 2012-06-08

 Question: Dear Sir, I want to know some examples of wavelet transforms in power system protection field.I am from power system specialization of electrical engg. By: mnrathod     Date: 2012-06-14 Answer: There are several researchers who have investigated the applications of wavelets in power system transients. There are two immediate domains which I can think of - in analyzing transient patterns and in analyzing the period-to-period variation of waveforms that are supposed to be periodic. If I understand correctly (I am not an expert in power systems), power system protection will require the analysis of transient patterns to detect possible faults. Wavelets have been used successfully there. By: Prof. V.M. Gadre     Date: 2012-06-22

 Question: Dear Sir, What is the difference between length and order with respect to filter design?are they related to the number of elements in the filter structure?Is there anything like zero order filter? By: ManojNiranjan.P     Date: 2012-06-26 Answer: Good question. Length normally refers to the length of the impulse response. For FIR filters, order = length - 1. For IIR filters, the length is always infinite! However, order in a more general case refers to the number of un-cancelled poles in an IIR filter. The terms 'numerator order' and 'denominator order' are also sometimes used to distinguish these two self-explanatory ideas. To be precise, the 'element cost' of implementation of a rational filter is measured by its 'numerator order' + its 'denominator order'. A 'zero order' filter will simply be an amplifier. Its frequency response will be of constant magnitude. By: Prof. V.M. Gadre     Date: 2012-07-01

 Question: Respected Sir,What is the value of u(t)[unit step function] at t=0? By: Hari     Date: 2012-07-08 Answer: The unit step is discontinuous at t=0. Its value at that point is undefined. That does not affect its behaviour under the integral sign, though. By: Prof. V.M. Gadre     Date: 2012-07-13

 Question: Sir, How to judge about linarity and time invarient Property from given Impulse response. Ex. h(n) = e^(-n)*sin(n*pi/6)u(n) By: Vijay Mukati     Date: 2012-07-12 Answer: One can, in principle find out the impulse response of almost any system. However, only for linear time-invariant systems, can one use the impulse response to characterize the system completely. By: Prof. V.M. Gadre     Date: 2012-07-13

 Question: Sir is there any practical realization of unit impulse signal in continuous domain?? By: sharad tripathi     Date: 2012-07-26 Answer: You could think of it as approximated by what happens, when many sine waves with frequencies close to one another come together, all reaching their maximum at time = 0. The other way is to think of it as a very narrow pulse through a gating circuit, constructed out of op-amps. By: Prof. V.M. Gadre     Date: 2012-07-28

 Question: Dear Sir, suppose after solving for response of a continuous LTI system to a bounded input i'm getting an impulse function with other terms, is that fatal for a system? If not how it can be interpreted physically? By: Raman     Date: 2012-07-30 Answer: Getting an impulse in the response to a bounded input indicates instability, since the output is then not really bounded. By: Prof. V.M. Gadre     Date: 2012-08-03

 Question: Can we have real life examples the DSP?? By: Sibghatullah Khan     Date: 2012-08-01 Answer: Certainly - look at mobile phones with advanced features, look at MPEG players ! By: Prof. V.M. Gadre     Date: 2012-08-03

 Question: Dear Sir, What is the relation between Fourier Series and Fourier Transform? By: ManojNiranjan.P     Date: 2012-08-03 Answer: The Fourier series is meaningful only for periodic signals. The Fourier Transform could be viewed as a limiting case of the Fourier series with the fundamental frequency tending to zero or the period tending to infinity. By: Prof. V.M. Gadre     Date: 2012-08-03

 Question: Respected Sir, What should be the starting point to study DSP .Pls Suggest a very basic book in DSP. By: Sibghatullah Khan     Date: 2012-08-04 Answer: I suggest you read the text on Digital Signal Processing authored by Johnny R Johnson. By: Prof. V.M. Gadre     Date: 2012-08-12

 Question: Respected Sir, Thank you for suggesting basic book in DSP.Sir Pls Suggest me a very basic book in Signals and System . Thanks in Advance. By: Sibghatullah Khan     Date: 2012-08-21 Answer: Dear Sibghatullah, The book by Oppenheim, Willsky and Young is fairly basic. The book by Lathi is good from the point of view of excellent illustrations from real life systems and down-to-earth explanations. There is actually a book by Nagrath and some others from BITS Pilani which I also liked, because they had given good numerical examples and practical illustrations. By: Prof. V.M. Gadre     Date: 2012-09-02

 Question: Dear Sibghatullah Khan,The best way to learn Digital Signal Processing and signals and Systems is to "learn from V.M.Gadre Sir Video Lectures" You can get these Videos from CDEEP-IITB (Centre For Distance Engineering Education Programme ).I have also requested Sir to give those courses thro NPTEL By: ManojNiranjan.P     Date: 2012-08-28 Answer: Dear Manoj, I appreciate this feedback. It is very valuable to me. It is because of enthusiastic and committed viewers like you that I feel satisfied with this effort and feel like doing more. Thank you once again. With warm regards. Gadre. By: Prof. V.M. Gadre     Date: 2012-09-02

 Question: define statistical variance and covariance By: ragish     Date: 2012-09-06 Answer: A little outside the scope of this course. Anyway, Statistical variance: the expected value of the squared deviation of a random variable from its mean. Statistical Co-variance of two random variables: the expected value of the product of the deviations of the two random variables from their respective means Please look up any standard text on probability and statistics for more details By: Prof. V.M. Gadre     Date: 2012-09-07

 Question: Respected sir, regarding stability of a system y(t)=d/dt x(t),what kind of bounded input is given to test the stability of a system.if u(t) is given impulse is comming and if sine signal is given cos is comming which is bounded signal.what kind of input is given to check the stability of a system. By: kiran     Date: 2012-09-10 Answer: The best example demonstrating instability of the differentiator is the bounded, analytic input: x(t) = sin(a t^2) that is, the sine of any multiple ('a' times) the square of time t. It is clearly bounded by 1. However, its output is: 2at cos (a t^2)which is clearly unbounded. This clearly indicates instability with a reasonable input. However, one could use the square wave, but the square wave is not differentiable in the sense of functions. We have to take recourse to the generalized function, the impulse which is of course, 'unbounded' if you wish to call it that. By: Prof. V.M. Gadre     Date: 2012-09-14

 Question: Respected sir,A periodic signal x(t),period T can be represented as a linear combination of e^(jkwt),for all integer k. But, while finding its component Ck at e^(jkwt) by using analysis equation and putting the value of x(t) from synthesis equation, we take the limit as 0 to T. But why not -∞ By: Anindya Sarkar     Date: 2012-09-16 Answer: Dear Anindya, For a periodic signal, we are dealing with the restricted space of such signals confined to a period, to make them square integrable/ absolutely integrable and so on. All the inner products, norms should then be calculated in this restricted period and not from (minus infinity). By: Prof. V.M. Gadre     Date: 2012-09-23

 Question: Sir please suggest one good book covering all the material discussed in your lectures. By: Saleem     Date: 2012-09-30 Answer: Dear Saleem, We (a colleague from Pune and I) are writing a book that will cover this material. We shall keep all of you informed on the progress of the book. Thanks for your interest. By: Prof. V.M. Gadre     Date: 2012-10-07

 Question: 1.What is the difference between Power spectral density(PSD) and Energy spectral density(ESD)?is the right side of the Parseval's theorem gives ESD? 2.Then how to convert it to PSD? 3.Is the output of modulus of FFT OR modulus square is related to PSD? By: ManojNiranjan.P     Date: 2012-10-03 Answer: Dear Manoj, Power spectral density and energy spectral density are respectively relevant for signals for finite power but infinite energy; and signals with finite energy. Parseval's theorem needs to be interpreted accordingly. It is the modulus SQUARED of the FFT which indicates PSD/ ESD. By: Prof. V.M. Gadre     Date: 2012-10-07

 Question: Sir, can you please explain me the relation between fs(sampling freq) ,f(signal freq), and N(number of FFT points)? By: ManojNiranjan.P     Date: 2012-10-03 Answer: Dear Manoj, If the number of FFT points is N, then the spacing between the points on the actual frequency axis, is 'sampling frequency divided by N'. By: Prof. V.M. Gadre     Date: 2012-10-07

 Question: respected sir how to calculate the fourier transform of cos(at^2). By: kiran     Date: 2012-10-12 Answer: It is a little involved. This is essentially a linear Frequency modulated function. Look up the calculation of the spectrum of FM waves in a standard text on communication. Normally these explain the calculation for a single tone modulation, but here you have a linear FM. In a single tone modulation, you would have to use Bessel functions. You could also try to 'complete the square' in the phase term of the Fourier integral, after decomposing cos(..) into a sum of two exponentials and proceed therewith. Please note that the Fourier transform would not be a function in the standard sense, generalized functions would have to be employed. By: Prof. V.M. Gadre     Date: 2012-10-21

 Question: Sir, If two signals are convoluted then what will be the Bandwidth of resultant signal? By: Arun Kumar     Date: 2012-10-20 Answer: Typically, the intersection of the bands of the two signals, since the Fourier Transforms get multiplied. Note that 'bandwidth' may not be defined for one or both the signals. By: Prof. V.M. Gadre     Date: 2012-10-21

 Question: Sir, What are the practical uses of Laplace & Fourier Transform? Which One is better? If Laplace transform is the general case then What is the need of Fourier Transform? By: Arun Kumar     Date: 2012-10-20 Answer: The Fourier Transform can be obtained from the Laplace Transform only if the Fourier Transform exists and is analytic. Take the standard ideal filters, the Fourier Transform of the impulse response (frequency response) is not analytic, it has a discontinuity. In that case, we could perhaps make a continuation to the entire complex plane, to get a Laplace transform but that is not useful at all. The Fourier Transform gives important sinusoidal component insights, indicates spectral requirements and processing needed. The Laplace Transform indicates possibilities for realization. Each has its own importance. By: Prof. V.M. Gadre     Date: 2012-10-21

 Question: Sir, Laplace transform exists for both real & imaginary axis. Does Real axis mean "Cos" terms? other than this what does it mean? what is the significance of imaginary axis? By: Arun Kumar     Date: 2012-10-22 Answer: The real axis of the Laplace variable gives the decaying/ growing exponential time term. The imaginary axis gives the oscillatory, sinusoidal term associated with or multiplying the exponential. By: Prof. V.M. Gadre     Date: 2012-10-26

 Question: Sir, what is the concept of negative frequency? in practical life, can we visualize it? if yes then how? By: Arun Kumar     Date: 2012-10-22 Answer: A sinusoid, cos(wt) comprises of a 'positively rotating' phasor exp(jwt) combined with a 'negatively rotating' phasor exp(-jwt). Only when these come together, is a sinusoid formed. It is mathematically more convenient to deal with phasors than sinusoids directly. Thus 'positive' and 'negative' frequencies refer to the frequencies of the phasors, not the sinusoids. 'Negative' frequency is as real or imaginary as 'positive' frequency in this sense. By: Prof. V.M. Gadre     Date: 2012-10-26

 Question: Sir, which book should i refer for Signals & Systems and Communication engineering and Digital signal processing? By: Arun Kumar     Date: 2012-10-22 Answer: Look up standard textbooks recommended for study in the Graduate Aptitude Test of Engineering (GATE) by the IITs. That could be an indicator. By: Prof. V.M. Gadre     Date: 2012-10-26

 Question: Sir, what is an analytic function and what is its significance? By: Arun Kumar     Date: 2012-10-22 Answer: An analytic function has continuous derivatives of all orders 'almost everywhere', to speak informally. It refers to a function which is just about as smooth as it can get - examples are sinusoids, exponentials. By: Prof. V.M. Gadre     Date: 2012-10-26

 Question: Dear Sir, Where I can find the application of Multirate DSP's and wavelets in the field of Medical Imaging By: Amitava     Date: 2012-10-24 Answer: There was a whole special issue of the IEEE Transactions on Medical Imaging, circa 2005 or so, devoted to the Applications of Wavelets in MRI! There was a similar special issue of the IEEE Journal on Selected Areas in Biomedical Engg (or some such similar name) around the late 1990s devoted to wavelets/ time-frequency methods in Biomedical Engineering. Even in special issues of the IEEE Proceedings (April 1996), IEEE Trans on Information Theory (March 1992) there have been papers devoted to the application of wavelets in MRI/ Biomedical applications. By: Prof. V.M. Gadre     Date: 2012-10-26

 Question: sir, what is the difference between audio,voice and speech By: kiran     Date: 2012-11-05 Answer: Dear Kiran, 'Audio' is much more than speech -it could include music, percussion and almost anything systematically generated in the audible range by humans. Speech is human communication using an underlying language, with focused intent. Voice is the medium in the human body for speech. By: Prof. V.M. Gadre     Date: 2012-11-11

 Question: Sir, What are the unit of Fourier Series, Fourier Transform, DTFT, DFT & DFS? By: Arun Kumar     Date: 2012-11-06 Answer: Dear Arun, DTFT and DFT work with normalized frequencies, so 'radians' or Hz/Hz can be thought of as 'units'. They are not really units, as the frequency is normalized. For the Fourier series, the unit is the same as the original signal as the expansion is in the same domain. For the Fourier Transform, the axis corresponds to frequency (Hz) or angular frequency (radians/sec). By: Prof. V.M. Gadre     Date: 2012-11-11

 Question: Sir, in analog domain we have Fourier as well as Laplace transform.LT is a better tool than FT. we can put s=jw for signals having FT. Why should we still learn FT? What is its significance? By: Rahul R Nair     Date: 2012-11-17 Answer: See my answer to the question by Arun Kumar on 21-10-2012. The Fourier Transform gives insights, which the Laplace Transform sometimes cannot. For example, look at the ideal filters - lowpass, bandpass, and so on. The Fourier Transform immediately tells us what the sinusoidal response should be, which is what the filters are supposed to do, in the first place. The Laplace Transforms of the impulse responses can probably be evaluated in some complicated way to yield non-analytic functions. However, they would not give meaningful or easily understandable interpretations. By: Prof. V.M. Gadre     Date: 2012-11-23

 Question: Namaskaar Sir, I wanted to know how to realize a higher order analog transfer function. I could see on the web how a first order transfer function is realized and even the higher order transfer functions were realized by cascading the first order components, but isn't there any other way without i By: Mahesh Murty     Date: 2012-12-09 Answer: Look up a text on 'Network Synthesis', example, the one by Van Valkenburg. There are several approaches to synthesize positive real functions based on L,C,R elements. By: Prof. V.M. Gadre     Date: 2012-12-24

 Question: Why we perform inverse z transform and what is the use of it?what if we use the signal in frequency domain? By: laiza     Date: 2012-12-13 Answer: The inverse z-transform is required for going back to time from the z-domain. All signals cannot be expressed in the frequency domain, exponentially growing signals are a counter-example. By: Prof. V.M. Gadre     Date: 2012-12-24

 Question: Sir, What is the difference between DFS & DFT? By: Arun Kumar     Date: 2012-12-17 Answer: It is essentially a difference in perspective. The DFT corresponds to a finite length signal. However, the inverse DFT expression, treated as a function of the time index, is periodic in the time index and is hence termed a DFS (Discrete Fourier Series). This is a manifestation of time domain aliasing. By: Prof. V.M. Gadre     Date: 2012-12-24

 Question: What is DCT? Why we use it & what is it used practically? By: Arun Kumar     Date: 2012-12-17 Answer: The DCT (Discrete Cosine Transform) is a small modification of the DFT where only real basis sequences, constructed out of sinusoidal sequences, are used. It is much more amenable to efficient implementation, when real data processing is a must. By: Prof. V.M. Gadre     Date: 2012-12-24

 Question: What are advantages & disadvantages of DCT over DFT? By: Arun Kumar     Date: 2012-12-17 Answer: Essentially the real data processing convenience. By: Prof. V.M. Gadre     Date: 2012-12-24

 Question: Sir, If there are N samples and we again resample them, then what will be minimum no of samples after resampling? By: Arun Kumar     Date: 2012-12-17 Answer: I do not understand the question properly. On what basis are you 'resampling'? Please clarify or reframe the question in more detail. By: Prof. V.M. Gadre     Date: 2012-12-24

 Question: Sir, I am student form Civil Engineering background and I am working on wavelets. Your lectures are of lot of help. Can you kindly tell a book that goes in sync with what is going on in lectures and for a non-electronics student like me? Thank you sir. By: Karthik     Date: 2012-12-24 Answer: Good to know that the lectures are helpful to you. Prof Aditya Abhyankar and I are trying to put a book together based on the series of these lectures. We could send you a very raw form of the book if it helps. You could give us feedback on the content and suggest how it should evolve. This is a general offer to all readers/ audience of our lectures series on this site. You will need to mention your email and give a brief background of yourself to enable us to know who is making the request. You can write to me on the email addresses: vmgadre@ee.iitb.ac.in, vmgadre2012@gmail.com By: Prof. V.M. Gadre     Date: 2013-01-04

 Question: Sir, I am student form Civil Engineering background and I am working on wavelets. Your lectures are of lot of help. Can you kindly tell a book that goes in sync with what is going on in lectures and for a non-electronics student like me? Thank you sir. By: Karthik     Date: 2012-12-24 Answer: same as your previous question - already answered By: Prof. V.M. Gadre     Date: 2013-01-04

 Question: Sir what is the difference between convolution & correlation and auto correlation and what are the practical uses of these? By: Arun Kumar     Date: 2012-12-28 Answer: Correlation of x(t) with y(t) is akin to convolution of x(t) with y(-t). Autocorrelation of x(t) = Correlation of x(t) with x(t). The autocorrelation indicates the 'similarity' of a signal with its own translates. Cross-correlation of two signals indicates their mutual 'similarity' at different translations. By: Prof. V.M. Gadre     Date: 2013-01-04

 Question: Sir, You have mentioned the value of u(t) at t=0 as undefined. But there are some authors they defined the value of u(t) at t=0 as 1/2. They could come this conclusion by taking average at t=0. I request you to explain this. By: Dr. Ravindra     Date: 2013-01-02 Answer: If one writes a Fourier series for a periodic square wave and seeks the limit of the series at the point of discontinuity, the limit is shown to converge to the average of the two values across the discontinuity. One could extend this to the Fourier Transform in the generalized sense for the unit step and ask whether its inverse yields a limiting value at the discontinuity. That is probably the line of thought. The other way to understand is to treat the unit step as comprising of a 'DC' part and a 'zero average AC' part - the 'DC part' is the average = 1/2, the 'zero average' AC part takes the value 1/2 for t>0 and (-1/2) for t<0. By: Prof. V.M. Gadre     Date: 2013-01-04

 Question: 1) Sir, is there a criteria for selection of wavelet basis to use for any analysis? 2) How can one decide up on the number of components to which a signal can be decomposed? By: Karthik     Date: 2013-01-10 Answer: 1. Certainly. In fact, you could look up a paper in the March 1992 issue of IEEE Trans Information Theory on Optimal Choice of wavelets for signal representation. 2. The length, in case of a finite length sequence, puts a constraint. Every time you decompose, you are halving the length of individual sub-band components. By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: By: Arun Kumar     Date: 2013-01-11 Answer: Question blank By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: Sir, What type of questions are asked from Random Variable in interview? Could you please tell me any website in which this type of info is given? By: Arun Kumar     Date: 2013-01-11 Answer: Not relevant to this forum. By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: Sir, How can we relate DFS and DFT to Energy & Power signal? By: Arun Kumar     Date: 2013-01-12 Answer: DFS and DFT are relevant only for 'power' sequences, their energy would diverge. By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: Sir, why is it difficult to analyze low frequency signal using Analog Signal Processing rather than DSP? By: Arun Kumar     Date: 2013-01-12 Answer: That is not true. One could analyze it easily using analog techniques at times. What Digital Processing offers in general, is flexibility, versatility and easy upgrade/ metamorphosis By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: Sir, What is Normalized frequency? What is its significance and how to calculate it? By: Arun Kumar     Date: 2013-01-14 Answer: Normalized frequency is the ratio of the actual frequency to the sampling frequency. It is used to build Discrete System Theory independent of the sampling rate. By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: What is the significance of Prob Distribution Function and Prob Density Function and what is the relation between them? By: Arun Kumar     Date: 2013-01-14 Answer: Typically, probability 'distribution' function is often used to denote the cumulative distribution, which is the running integral of the probability density function from minus infinity to the argument value at which it is being calculated. At any given value of the random variable, the cumulative distribution refers to the probability that the random variable could be less than that particular value. By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: Sir, In the derivation of fourier transform from fourier series(assuming period to be infinite),the coefficients obtained are almost zero. So my question is how are these coefficients significant? since x(jw) gives value of C*T where T tends to infinity and c is coefficient. Please explain By: Girish Barman     Date: 2013-01-23 Answer: I am not clear why you feel that the coefficients are almost zero. Is it because you think that the integral is divided by T, which tends to infinity? But then that is again annulled by the fact that you are bringing impulses arbitrarily close together - and the division by T is absorbed in the 'impulses merging', so to speak. The Fourier Transform can be non-zero over a significantly large region of support in general. Maybe you could pose your question more specifically/ differently after reading this answer. By: Prof. V.M. Gadre     Date: 2013-02-01

 Question: Sir, regarding choice of wavelet, i have found that the highest cross correlation between wavelet function and signal is the best suited wavelet for that signal. Is that the right way or should I go with the paper which you have suggested? If right kindly explain how this can be done sir. By: Karthik     Date: 2013-02-05 Answer: One way is indeed to look for a wavelet that is most 'similar' to the signal, which can be determined by looking at the cross correlation with a normalized signal. That would often give the most compact representation. However, that may not be the only consideration. One may want to find the best wavelet to determine specific features that can help classify or characterize the signal/ image. In that case the considerations for choice of wavelet will be different. By: Prof. V.M. Gadre     Date: 2013-03-03

 Question: Sir, I want to re frame my second question that I asked on 10-01-13. How can one fix the level up to which a signal can be decomposed in case of usage of DWT. I mean, the optimum number of decompositions sir? Is there a difference between Fast Wavelet Transform and DWT? By: Karthik     Date: 2013-02-05 Answer: One can broadly determine the level upto which a signal can be decomposed depending upon two considerations: one, how much data one has to decompose as the data gets halved at each decomposition; and second, the extent to which one wishes to get frequency resolution at lower frequencies. The Fast wavelet transform is an efficient way to IMPLEMENT the discrete wavelet transform. It is not a different transform. By: Prof. V.M. Gadre     Date: 2013-03-03

 Question: DearSir,Thanks for making this forum very active.Iknow its very difficult,with your busy schedule,personal work to answer the queries here.But still you do it perfectly well.Thanksfor this spirit.I pray for this to continue for many decades to come with new courses too.Thanksfor everything!like u By: ManojNiranjan.P     Date: 2013-02-19 Answer: Thank you very much for these encouraging words. Believe me, it is the encouraging response from you and everyone else on this forum that makes me want to answer queries as regularly as I can. It makes me very happy to see many people in different places using these lectures and this forum. God bless you. By: Prof. V.M. Gadre     Date: 2013-03-03

 Question: Can I be able to separate music and voice signals from the song after listening to these lectures By: sravyabhogavilli     Date: 2013-03-05 Answer: Certainly but you could also probably do that without listening to the lectures. Please listen to the lectures for much more, that just this little objective. Else you will miss much of what is being explained, on account of a fixation on a very narrow objective! By: Prof. V.M. Gadre     Date: 2013-03-24

 Question: Respected Sir, in your lecture no. 31, while discussing WPT, you gave example of 0 to pi spectrum. Can you please tell me the reference of the same. Secondly i want to know the guidelines for wavelet selection & I want to know more about vanishing moments.suggest book. Pravin Kulkarni,PVG Pune. By: Pravin Kulkarni     Date: 2013-03-13 Answer: Not sure what you mean by the 0 to pi spectrum. I think what you are referring to, is a 'prototype' spectrum which has distinct amplitudes at each frequency between 0 and pi. A simplest example of such a spectrum is one whose magnitude varies linearly from 0 to pi. I have used that to illustrate many filter bank operations. Vanishing moments refer to the degree of the polynomial which can be 'annihilated' (reduced to zero) at the output of the highpass filter of the analysis filter bank. I suggest you take any text/ reference which discusses how the Daubechies' filters are constructed. They have an increasing number of vanishing moments with an increase in order. I have also explained these in my NPTEL lectures where the Daubechies' filters are derived. By: Prof. V.M. Gadre     Date: 2013-03-24

 Question: Sir,I want to select best wavelet for my signal among available wavelet families using cross correlation between wavelet and signal.In that case, do I have to compute CWT of signal? If so, for how many scales do I have to compute? If its not the method, could you kindly let me know how to correlate By: Karthik     Date: 2013-03-19 Answer: Yes, the CWT is the natural choice if you wish to see the cross-correlation of the signal with a wavelet at different scales and translates. The scaling and translation parameters are continuous in the CWT. To get an idea of the scale range to work with, you will need some a-priori knowledge of the signal spectrum. Remember, a particular scale parameter value corresponds to a certain range of frequencies, based on the bandpass nature of the wavelet. By: Prof. V.M. Gadre     Date: 2013-03-24

 Question: Sir, we know that a discrete-time sequence has values only at integer time instants like -1,0,1,2,3,..... Now, if we have a sequence which is defined for n = 0.25, 0.5, 0.75, 1, 1.25, 1.5 and so on, can we call it a discrete-time sequence? Further, can we use the letter \'n\' for its time index? By:     Date: 2013-03-19 Answer: Yes, indeed, a sequence defined only at discrete, isolated instants is a discrete-time sequence even if the points at which it is defined do not coincide with the integers. In the particular example which you give, the sequence is still uniformly spaced with a spacing of 0.25 between samples. One could also conceive of a non-uniformly sampled discrete time sequence. A theory to deal with that kind of sequence, would be more difficult than standard discrete system theory. By: Prof. V.M. Gadre     Date: 2013-03-24

 Question: Sir, what is the physical significance of the \'s\' and \'z\' domains? Do they exist in reality? By:     Date: 2013-03-21 Answer: The 's' and 'z' domains are parameter domains for complex continuous time and discrete time exponentials respectively. Yes, realistic linear shift-invariant systems exhibit decaying exponentials for their natural responses. It becomes meaningful to characterize systems in terms of these exponentials, and therefore the 's' and 'z' planes. By: Prof. V.M. Gadre     Date: 2013-03-24
 Disclaimer: We will take every effort to answer your question.However, in case of delay or no response NPTEL claims no responsibility. Site Maintained by Web Studio, IIT Madras. Contact Webmaster: nptel@iitm.ac.in