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I would simply say that it doesn't matter so much. The Fourier Transformation and its inverse are a pair and the two formulas are entangled and require a normalization factor, which is up to conventions. See eg enter link description here If your theory/model does not require a special convention, it is basically a degree of freedom that you can choose to ...


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Your code has some troubles, and perhaps also your theoretical understanding. Let me put here a mini summary of observing a practical sine wave and its frequency spectrum using FFT function of MATLAB / Octave. Assume that there's a continuous-time ideal infinitely long sinusoidal wave with frequency $\Omega_0$ given as: $$ x(t) = A \cos(\Omega_0 t) , \tag{...


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The best way to accomplish your desired result is to estimate the parameters of the interfering tone(s) and remove it(them) from the signal in the time domain. To get you started on how to go about this, I recommend you read these two articles of mine: Two Bin Exact Frequency Formulas for a Pure Real Tone in a DFT Phase and Amplitude Calculation for a Pure ...


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It depends on what you mean by SNR. It's a common joke in the DSP community to spell it out as "something to noise ratio", referring to the fact that there is no unique definition of SNR, so the term by itself means nothing. Define it yourself and use it appropriately. What's common is to define it as ${\rm SNR} = \frac{P_{\rm s}}{P_{\rm n}}$ where $P_{\rm ...


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The sharp peaks are actually due to segmentation and concatenation, you need to have overlapping segmentations. The peaks occur on the edges of segments mostly. In following figures I tried to show what I mean, blue curve are hamming function coefficients. I do not why, but if it is essential to process your signal in segmented mode, you should consider ...


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There is no reasonable way to explicitly choose the number of taps before and after the peak. The reason is simple: the arbitrary magnitude response design results in a linear phase, and, consequently, the impulse response is symmetrical. If you specify a desired complex frequency response in terms of magnitude and phase, the location of the peak is an ...


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negative group delay is merely in relation to a greater more positve delay. If energies in a region fc1 are delayed by group delay of 5ms and another region fc2 have a group delay of -3ms, the fc2 will arrive 8ms before fc1 by virtue of having passed through the filter.


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ARM provides efficient reference implementations of different DSP processes, including IIR: https://arm-software.github.io/CMSIS_5/DSP/html/index.html You can try them out and evaluate which is best for your purposes by checking performance and memory consumption. You could probably optimize for your specific application, but I wouldn’t bother unless it ...


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Here are 3 points that you must consider : 1 - What is the minimal latency you can tolerate? This is important, as it's important to know whether to need process every sample as fast as possible or if you can perform batch processing which is typically more efficient but creates latency . 2 - No matter if you implement the IIR in fixed-point or floating-...


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Regarding your integral, it is not quite correct I think. You used partial integration to solve it, which works. Let's consider $\int t {\rm e}^{-\jmath \omega t}{\rm d}t$ and call $f(t) = t$ and $g'(t) = {\rm e}^{-\jmath \omega t}{\rm d}t$ so that $g(t) = -\frac{1}{\jmath \omega}{\rm e}^{-\jmath \omega t}$. Then using $$\int f(t) g'(t){\rm d}t = f(t)g(t)-\...


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