# Tag Info

Accepted

### “The Fourier transform cannot measure two phases at the same frequency.” Why not?

It's because the simultaneous presence of two sinusoidal signals with the same frequency and different phases is actualy equivalent to a single sinusoidal at the same frequency, but, with a new phase ...
• 28.3k
Accepted

### Why is the time domain low-pass filter the "sinc" shape?

It is a good way to understand the lowpass behavior of sinc function (as well as the convolution) through visualization. I've made some modification on this animated convolution project and here are ...
• 3,253

• 1,802
Accepted

### Fast & accurate convolution algorithm (like FFT) for high dynamic range?

Disclaimer: I know this topic is older, but if one is looking for "fast accurate convolution high dynamic range" or similar this is one of the first of only a few decent results. I wanna ...
• 175
Accepted

### Can FFT tells us existance of same frequencies with different phases?

I am thinking of two numbers. They add to the number 15. Tell me what the two numbers are.

### Why is the time domain low-pass filter the "sinc" shape?

One way to think about it is the requirement of what a filter does, and what is the relation between the time domain and frequency domain plots of the signal or the filter. This also requires to know ...
• 2,321
Accepted

### How to prove that the peak of the autocorrelation function is at zero lag?

The Cauchy Schwarz inequality states that: $$\left|\int_{-\infty}^{\infty}g_1(t)g_2(t) dt\right|^2 \leq \int_{-\infty}^{\infty}|g_1(t)|^2 dt \int_{-\infty}^{\infty}|g_2(t)|^2 dt$$ I'm going to ...
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• 7,590
Accepted

### Fourier series of cycloid

The Fourier series of the cycloid can be expressed in terms of the Bessel functions of the first kind: $$J_n(x)=\frac{1}{\pi}\int_0^{\pi}\cos(nt-x\sin t)dt,\qquad n\in\mathbb{Z}\tag{1}$$ Using the ...
• 90.8k

### Why is the time domain low-pass filter the "sinc" shape?

Perhaps one way to see the sinc is as a special moving average filter. As you noted, the lower the cutoff frequency (filtering out higher frequencies), the wider the sinc mainlobe. This corresponds to ...
• 1,945
Accepted

### Can use of Fourier transform be minimized completely with the help of Laplace and Z transform?

The answer to your last question is definitely 'no'. The point hotpaw2 makes in his answer is very relevant: the FFT is an efficient implementation of the DFT, and there are no equivalently efficient ...
• 90.8k

### "Fourier Transform can localize signals in frequency domain, but not in time domain." -- What does it mean in layman's terms?

To localize here means: to find where the signal is mostly concentrated, and with what precision. This could be either in the time or the frequency domain. An answer could be: the signal's center of ...
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### Real world application of signal sparsity?

Sparsity concept is extensively being used in computer vision and image processing. The Idea is that natural image can be pretty sparse when it is transformed to different bases. this bases can be ...
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### Fast & accurate convolution algorithm (like FFT) for high dynamic range?

Rather than scrapping the fast convolution algorithm, why not use an FFT with a higher dynamic range? An answer to this question shows how to use the Eigen FFT library with boost multiprecision.
• 3,040