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Accepted

Bandwidth of an entire song

First of all, kudos to you: I appreciate the effort and thinking you've managed to articulate in your question. The DFT is a mathematical tool. As such, the parameters used to compute it can hide or ...
• 6,644
Accepted

Why doesnt DFT Padding cause sinc like features

The OP is showing very good insight in all the comments stated. A product in the time domain with a rectangular pulse is convolution in the frequency domain with a Sinc. In fact zero padding in time ...
• 53.8k
Accepted

Why zero-pad at the end of a signal?

What differences does it make? In one line - The phase information of the Fourier transform changes. Explanation: Adding zeros at the start of the signal translates to adding delay. Consider the ...
• 665

How Best to Characterise a Window Function

An oldie but a goodie it fred harris's "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform". It has a nice table showing different figures of merit for different ...
• 25.9k
Accepted

FFT: Sinewave frequency displacement when zero-padding

(I show only positive frequencies): which is part of the problem here :-) You would get the expected behavior if you used a complex sine, i.e. $x[n] = e^{j2\pi\frac{n}{N}}$ but a sine wave actually ...
• 47k
Accepted

Why are my frequency bins oscillating?

This is indeed spectral leakage and specifically the dependency of the leakage on phase. Here is an example of 30 Hz sine with with a random phase. These are 50 frames with a randomized phase. The &...
• 47k

@gschro, I understand your puzzlement. Find the equation for computing a DTFT, in a textbook or on the Internet, and carefully examine it. In that equation $omega$ is a continuous frequency variable ...
• 5,857
Accepted

On the left side of Figure 3-21(a) the discrete 16-sample input sequence is represented by the dots. (The lightly-shaded sinusoidal curve is shown for reference only!) On the right side of Figure 3-21(...
• 5,857

Discrete Fourier Transform of the Gaussian

The (continuous-domain) FT of a Gaussian is a Gaussian, as OP knows. To get the DFT pair from a FT pair we need to sample and crop the time domain, which is equivalent to replicating and sampling the ...
• 2,720

Why are my frequency bins oscillating?

The idea that you're looking for here is spectral leakage. As alluded to in the comments, the DFT bins will undergo different amounts of spectral leakage depending on the initial phase of the tone ...
• 1,432

Why doesnt DFT Padding cause sinc like features

@George kirby. I suggest you discard that notion of "multiplying a step function on top of the original signal to form a longer time sequence". I believe such a multiplication is not ...
• 5,857

Why does the frequency sampling method for FIR filter design operate in this manner?

This is how I would define the frequency-sampling method. Assuming linear phase (to start with). Draw out your desired frequency response magnitude, with as much detail as you need to to define the ...