- Four types of FIR filters with generalized linear phase
- Windowed filter designs
- Parks-McClellan equi-ripple filters
Monday, November 29, 2010
Class: 11/29/2010
Saturday, November 20, 2010
Dr.Gunther,
As far as I know a LTI system is causal iff the ROC of a system function is the exterior part of the circle.Also a LTI system is stable iff ROC of a system function includes the unit circle.Then depending on this information, does it imply that the causal system can never be a stable system?
I request you to please explain me with the help of an example.
Thank you.
Tejas
As far as I know a LTI system is causal iff the ROC of a system function is the exterior part of the circle.Also a LTI system is stable iff ROC of a system function includes the unit circle.Then depending on this information, does it imply that the causal system can never be a stable system?
I request you to please explain me with the help of an example.
Thank you.
Tejas
Thursday, November 18, 2010
Lab 4 Questions
I have a few questions about lab 4. I'm not sure exactly what is meant by all of the inputs and outputs of step 5. Specifically:
INPUTS:
- a window
- an overlap factor
OUTPUTS:
- the spectrogram in a 2D array
- a time array
- a frequency array
Would you mind elaborating on these?
Is the "window" meant to be some sort of windowing filter to be applied to the time-domain signal?
Yes. One of the inputs is the FFT size. Let's call this N. The window is a length N array/vector of samples of the window that should be applied to the samples of the time-domain signal before the FFT is computed. If no window is to be applied, then the array/vector will be filled with N ones. We have talked about various types of windows in class including Kaiser, Hamming, etc. There are many more in the textbook.
Is the "overlap factor" meant to imply that as we take the FFT of the signal in chunks, the chunks will have some samples overlapping?
Yes, this is exactly as you describe. You split the signal into overlapping chunks of length N samples. The overlap is specified by one of the inputs. The window is applied to each chunk and the FFT computed.
Does "the spectrogram in a 2D array" mean that we should attempt to make a graphical representation of the spectrum using a 2D array and some arbitrary ASCII character? If so, should we plot the magnitude squared of the FFT output?
Each time you compute an FFT of a chunk of windowed data, you will get a spectrum array/vector out of the FFT. Stack these side by side in a 2D array.
I'm not sure what the "time array" would be unless you just want us to output the time domain samples as an array of doubles.
The time array is an array/vector of times in seconds (this is why you need to know the sample rate) of the firsts sample in each of the signal chunks. Given the sample rate, the FFT size N, and the number of samples of overlap, you should be able to compute the elements of the time array.
Is the "frequency array" just an array representing the outputs of the FFT? Since we will be performing multiple FFTs on the signal in segments, should we average the results of all of the FFTs? It wouldn't seem to make much sense to concatenate them. Also, since the FFT will yield a complex signal, should this array be an array of complex numbers, or should it be the real plus imaginary parts, or the magnitude, or the magnitude squared?
The frequency array/vector contains the FFT bin center frequencies multiplied by the sample rate. This gives an array of frequencies in Hertz. Remember that the FFT bin center frequencies are:
k/N for k=0, 1, 2, ..., N-1.
INPUTS:
- a window
- an overlap factor
OUTPUTS:
- the spectrogram in a 2D array
- a time array
- a frequency array
Would you mind elaborating on these?
Is the "window" meant to be some sort of windowing filter to be applied to the time-domain signal?
Yes. One of the inputs is the FFT size. Let's call this N. The window is a length N array/vector of samples of the window that should be applied to the samples of the time-domain signal before the FFT is computed. If no window is to be applied, then the array/vector will be filled with N ones. We have talked about various types of windows in class including Kaiser, Hamming, etc. There are many more in the textbook.
Is the "overlap factor" meant to imply that as we take the FFT of the signal in chunks, the chunks will have some samples overlapping?
Yes, this is exactly as you describe. You split the signal into overlapping chunks of length N samples. The overlap is specified by one of the inputs. The window is applied to each chunk and the FFT computed.
Does "the spectrogram in a 2D array" mean that we should attempt to make a graphical representation of the spectrum using a 2D array and some arbitrary ASCII character? If so, should we plot the magnitude squared of the FFT output?
Each time you compute an FFT of a chunk of windowed data, you will get a spectrum array/vector out of the FFT. Stack these side by side in a 2D array.
I'm not sure what the "time array" would be unless you just want us to output the time domain samples as an array of doubles.
The time array is an array/vector of times in seconds (this is why you need to know the sample rate) of the firsts sample in each of the signal chunks. Given the sample rate, the FFT size N, and the number of samples of overlap, you should be able to compute the elements of the time array.
Is the "frequency array" just an array representing the outputs of the FFT? Since we will be performing multiple FFTs on the signal in segments, should we average the results of all of the FFTs? It wouldn't seem to make much sense to concatenate them. Also, since the FFT will yield a complex signal, should this array be an array of complex numbers, or should it be the real plus imaginary parts, or the magnitude, or the magnitude squared?
The frequency array/vector contains the FFT bin center frequencies multiplied by the sample rate. This gives an array of frequencies in Hertz. Remember that the FFT bin center frequencies are:
k/N for k=0, 1, 2, ..., N-1.
Monday, November 15, 2010
Lab 4 Question
Russ,
That's right. Do NOT do the prime factor algorithm.
--Jake
Dr. Gunther,
The 4th instruction in the lab specification is as follows...
4.[SKIP] Write a prime factor FFT algorithm for N=N1 x N2 x ... x Nk where N1, N2, ..., Nk are a given list of relatively prime integers.
Does [SKIP] mean you don't want us to do this one?
Thanks,
Russ
That's right. Do NOT do the prime factor algorithm.
--Jake
Dr. Gunther,
The 4th instruction in the lab specification is as follows...
4.[SKIP] Write a prime factor FFT algorithm for N=N1 x N2 x ... x Nk where N1, N2, ..., Nk are a given list of relatively prime integers.
Does [SKIP] mean you don't want us to do this one?
Thanks,
Russ
Class: 11/15/2010
- Inverse z-transform
- Matlab functions: residuez, poly, roots, fliplr, flipud, zplane, filter(num,den,[1 0 0 0])
- Synthetic long division (filter)
Friday, November 12, 2010
Friday, November 5, 2010
Class: 11/05/2010
- Finished discussing bandpass sampling
- Introduction to the z-transform
- Relation to the DTFT and the DFT
- Region of convergence
Wednesday, November 3, 2010
Monday, November 1, 2010
Exporting class notes to PDF
I've noticed that in the PDF version of the class notes, the highlighted parts are illegible because the highlighter color isn't transparent to the text behind it. A solid yellow rectangle is covering up what was intended as the most important points of the lecture. Does anyone know of a way to recover what is behind the yellow in the PDFs? Has anyone tried it with other PDF readers besides Adobe?
Class: 11/01/2010
- Discrete-time processing of continuous-time signals
- Introduction to bandpass sampling
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