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How to evaluate DFT for a sequence extending from n=2 to say n=N+1? Formularistic: trivial variable substitution of the running variable $n$ by $\tilde n = n+2$, done. Looking at it as a signal: When doing an DFT, it helps to think of it simply as mapping of $\mathbb C^N\mapsto\mathbb C^N$, i.e. a complex vector goes in, same size complex vector comes out....


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Yes, they are the same. Let us take the linear convolution of $x[t]$ and $y[t]$ as 2 portions $H_1$ of length $N$ corresponding to first $N$ samples, and $H_2$ of remaining $N-1$ samples. Circular convolution between $x$ and $y$ causes $H_2$ to overlap over $H_1$ because of time-aliasing. So the first $N-1$ samples of the result is $H_1 + H_2$ with only the ...


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For any finite length DFT, to prevent aliasing, the sampling rate needs to be above (not equal to) twice the highest frequency in the signal.


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Goertzel in fact is the matched filter for a single frequency – so, it's, in the presence of uncorrelated noise, the estimator that gives the best estimation variance under fixed observation. But: for Goertzel to work, you need to use a number of samples that is an integer and a multiple of $f_\text{sample}/83\,\text{Hz}$. Unless your sampling rate hence ...


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I was wondering if my understanding of the DFT above is correct, Yes. This all seems correct although I recommend looking closely at the case of a sine wave that does not line up exactly with a frequency bin. There is a lot of insights and learning in that one and does this mean that, for each DFT bin, the DFT performs N summations and N multiplications ...


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Plain DFT performs N summations and N multiplications to give the amplitude of the frequency at that DFT bin but usually, we use FTT which is an algorithm for reduction of the number of multiplications. Since you project your signal on the complex exponent, your output is complex too. There are different ways to represent the output. You can decompose the ...


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There are a few possible answers depending on the signal and your meaning of "normal calculation". If the signal is stationary, then you might be able to use an old fashioned analog spectrum analyzer, the kind that works by sweeping a narrow-band analog filter across the input signal, and graphing the amplitude results on an X-Y pen plotter. Then you could ...


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I'm going to disagree with the fellows here. Big time. Yes you can in special cases. If your signal is a pure real tone (sinusoid) with a whole number of cycles in the DFT frame, all the DFT values will be zero except for a conjugate pair which are directly determinable by your tone parameters. If your signal is a pure real tone (sinusoid) with a non-...


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Let’s be clear on what we will refer to as time delay and phase shift. Due to the common association of individual frequencies as sinusoids many confuse delay and phase shift as being equivalent. However a phase shift in time is simply multiplying a time sample by $e^{j\phi}$ while a time delay is displacing the sample in time such as done with $x(t-\tau)$. ...


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pyo is not really the issue here at all. The question still stands if you were to substitute it with a million other packages of similar functionality. What is at the centre of this question is "How to build a classifier to distinguish between different types of hits on a drum". Once you have that sorted, you can then implement it with whatever package you ...


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Caveat: @Hilmar's answer is neat, I just offer a talkative version. A role of Fourier operations on data in any dimension is to provide an alternative (dual) description as "quantity of information" (let us say energy) per "frequency components". And frequency components can be defined in several ways (across each dimension, radially, etc.) The role of ...


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For 2-d input that is of similar nature in both dimensions (ie spatial pixels) and where you want to achieve something similar in both (eg find low frequency components) you probably want fft2(). As noted above, fft2() is functionally equivalent to doing a 1-d fft on the rows, then another 1-d fft one the resulting columns. -k


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They perform two different mathematical operations FFT executes a 1-dimensional Discrete Fourier Transform one each column of the input matrix (or the first non-singleton dimension) FFT2 executes a full 2-dimensional Discrete Fourier Transfrom on the entire matrix. Which one you want to use depends on your specific application. One is not inherently "...


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Since this is clearly homework, let's help you with hints: The set of tricks for such problems is typically pretty limited; try (and that's really what solves the issue) Multiplying the equation with elements from your right-hand term from left and/or right, so that identity matrices form. Writing your matrix/operator property down as structure of your ...


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