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We are analyzing a real signal with the DTFT. Since we are using a limited number of samples it's like we are transforming a finite signal. No. The DTFT takes an infinite discrete time signal as an input but the spectrum is continuous. I think you are confusing the DTFT and the DFT. They are different things. As I remember, the FT of a finite signal has ...


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If I have an output from band-pass filter and want to convert it back to time domain. Is it also the correct approach to cyclic shift to left and pad zeros in the middle before applying windowing and convert back to time-domain?


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Regarding your first comment, I have a figure that might help, in terms of intuition. It's a bit badly scaled but it might do the work.


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Of course you could. But I cannot find a useful manner. Because of duality, product or convolution in the image domain can be re-expressed as a convolution or product in the frequency domain. Also because if you apply it locally, components of a frequency transformation generally produce a value akin to intensity. In the extreme and trivial case, a one-...


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staying faithful to the subject "removing window effect in freq domain via convolution" (despite the OP perhaps wanted to achieve something else or something similar), I feel to add my comment having personal experience with this specific topic. Often I have the necessity to remove a Hann window in frequency domain, working in a STFT framework which uses ...


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Okay, I am not quite understanding your question. Let's start with the definition of the Gaussian, aka the Bell Curve, in its general form. $$ f(t) = \frac{1}{ \sigma \sqrt{2\pi}} e^{ -\frac{(t-\mu)^2}{2\sigma^2} } $$ $\mu$ is the mean, and represents where the peak occurs. $\sigma$ is the standard deviation, and identifies where the inflection points ...


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On a straight forward approach, energy of a signal given by $E = \int \limits_{-\infty}^{+\infty}|x^2(t)|dt$ is a constant number whereas PSD can be obtained from FFT which is a function of frequency. PSD is the square of the absolute value of FFT. In either case the value of energy or PSD gives an insight of the amplitude/strength of a signal.


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The basic idea is called - Music Finger Printing. Searching for it will yield many results. I'm attaching few good ones I found: How Does Shazam Work? How Does Shazam Work? Music Recognition Algorithms, Fingerprinting and Processing. Creating Your Own Shazam (Identify Songs) with Python Through Audio Fingerprinting (The YouTube Video). Audio ...


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