My All Signal Processing channel contains short lectures on topics in signal processing. Many of the lectures have also been used with an inverted or "flipped" classroom paradigm at the University of Wisconsin.
The playlists provide a systematic progression through the material. Each playlist includes a list of prerequisite playlists for understanding the background material.
What is the formula of u[n] in 3:26 such the a variable's value determes the value of x[n] such a way in each case,i don't understand. And why in 4:36 when you aply the z transform formula on to x[n] you write Sum n-oo to +oo a^n*z^-n instead of Sum -oo to +oo a^n*u[n]*z^-n suposed the x[n] is a^n*u[n] not only a^n ? I don't understand this neither.
This is a good overview of FFT. It would be nice to explain how the DFT convolution sum is derived. Also, the de-interlacing of the inputs was glossed over (not explained clearly) but only the reversed binary notation was mentioned (this is just an after-the-fact observation of How, not an explanation of Why). Readers who dive deeper into the splitting of a larger N-point FFT into two smaller N/2-point FFT’s, or understand the relationships between the twiddle factors (and their periodic nature) would understand and retain better the FFT technique (and be able to conquer any arbitrary size of N-point FFT (N being a power of 2, of course).
There are unknown way to visualize subspace, or vector spaces. You can stretching the width of the x axis, for example, in the right line of a 3d stereo image, and also get depth, as shown below. L R |____| |______| TIP: To get the 3d depth, close one eye and focus on either left or right line, and then open it. This because the z axis uses x to get depth. Which means that you can get double depth to the image.... 4d depth??? :O p.s You're good teacher!
Consider an at rest linear system described by y"+25y=2sint+5cos 5t The response of this system will be Decaying oscillations in time. Oscillatory in time. Growing oscillations in time: None of the above.
Hello, I need help clarifying two concepts. First, 4:31 makes perfect sense to me. We're just using the definition of Euler's Identity; if we wanted to re-expand back to regular Acos(x) + Aisin(x) notation, and our function didn't have an imaginary component, the second term would go to zero. I.e., I can represent any sinusoid with Euler - even if it doesn't have an imaginary component. This is nice because we can break up our sinusoid into time dependent & independent components. This makes perfect sense. Then, at 4:57 we seem to transition into something completely different. I understand the math for both, but I don't understand why I would use 4:57 over 4:31? What was wrong with just using Euler's Identity like 4:31? For example, at 7:59 I could have just as well used Euler's Identity like done at 4:31 instead of using this cos definition. Could you please help me connect these two ideas? Thank you, sir.
On advantage of the DTFT is its ability to provide greater frequency resolution with a single dominant frequency than the DFT for a given N. One application could be trying to use a dsp to accurately estimate the frequency of a guitar string for tuning to the proper pitch. We wouldn't want our tuner to be limited to only 1/T. Also, the small battery powered DSP cannot do an very large FFT for more resolution. Can you derive or simulate the resolution enhancement limits with the W(e(-jw) convolution?
One advantage of the DTFT is you get a continuous frequency domain. With a single dominating frequency, the peak frequency can be resolved with higher resolution than with the DFT with frequency samples of 1/T. Can you calculate or show a simulation of the limiting resolution of DTFT over the DFT based on your convolution of W(e^jw) factor? Give the same N.
Congratulations Professor Van Veen for your ability and beautful presentation! Mary Christmans nas Happy New Year! Gos bless you! Jacareí -Sao Paulo-Brasil
