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Accepted

• 80.2k
1 vote

FFT Artifacts and their cause beyond frequency resolution

The issue is probably that you're just zeroing out the FFT coefficients and then taking the inverse FFT. This is equivalent to multiplying the frequency domain by a response that is 1 everywhere ...
• 22.5k
1 vote

Basis Pursuit Denoising (BPDN) algorithm for Direction of Arrival Estimation

Check out SPGL1. It's probably the one most often used for basis pursuit/compressive sensing.
• 598
1 vote

What are the criteria for a change-of-basis transform to be doable in $O(n \log(n))$?

The usual reason you see $O(n \log(n))$ computations is when the $n^2$ direct-approach can be decomposed into two $n/2$ problems, and those can be decomposed into four $n/4$ problems etc. So the thing ...
• 22.5k
1 vote

What is the best way to decide whether a periodic signal is present in a noisy environment with a limited number of samples?

The problem you're running into seems to be that you have conflicting wants, specifically the fact that you want to operate at low SNR and use a small amount of samples. Integration gain needs to come ...
• 2,762
1 vote

Constructing an input signal whose response is determined by the impulse response

A more detailed proof based on Matt's answer. Let $n_0$ be the argument to $\max\{|y[n]|\}$, i.e. $\max\{|y[n]|\} = |y[n_0]|$. We can always find $x[n]$ as a series of +1's and -1's, s.t. |y[n_0]| = ...
• 43
1 vote
Accepted

Problem with the existence of inverse DTFT

You're absolutely right, the given system doesn't have a frequency response, at least not as a conventional function. There's a pole on the unit circle, so the system is not stable (actually, it is ...
• 80.2k
1 vote
Accepted

If $y(n)-y(n-1)=bx(n)$ is an LTI system, find $b$ such that $\left|H(e^{i\omega})\right|=1$ for $\omega=0$

After changing the given difference equation in your updated question, I don't see a problem anymore. Your answer is correct. If someone claims that $b=1$ is the correct solution, then have a look at ...
• 80.2k

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