# Tag Info

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Why normalized filters Last question first, "Why $1/\sqrt2$": Because it makes the (Euclidean) norm of the filter $1$, so that the whole wavelet filter bank operation (if done right, that is, the decimated version) is orthogonal/isometric. It is a design choice, there is nothing wrong in staying with the integer values and correct the combined factor during ...

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You may filter frequency band you are interested in and then downsample,so you won't lose much information. If that is not sufficient you can use filterbanks to process different frequency bands independently.

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this depends a lot how "good" this estimate needs to be. Here is a "rough & dirty" method. Put your scope in spectrum analyzer mode. Make sure you see all harmonics. Look where the highest harmonic is and that's still visibly sticking out over the noise floor. Quadruple that frequency and use this as your sample rate. Sample your signal for a sizable ...

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My suggestion: First, low-pass the signal @ 20 kHz. Then, since you are interested for a single component only, you could set up a Least-Squares estimation (in the time domain) for that particular component. You can take a look at the paper "Chirp rate estimation of speech based on a time-varying quasi-harmonic model" where you can process your signal in ...

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My suggestion: Segment the signal with consecutive windows calculate FFT for each window estimate FFT peaks. In your case only the first peaks is important the variation of the FFT peak (difference in peak location for two consecutive windows) over time (time difference between windows or window length) will give you the local slope. you can calculate ...

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I observe the following about your signal: of interest are only frequencies below 20 kHz there's but a single, very dominant tone in that – you've got excellent SNR The development of frequency over time is either constant, or a linear function of time So, from that, I'd propose the following steps: Low pass filter appropriately to restrict your bandwidth ...

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There could be a number of approaches for this task, depending on the number of channels (microphones) in your input and structure of available data. Given a labeled data set from a previously known set of rooms, you can train a neural network (NN) to classify in which one of them a new sample was recorded. A second approach would be to estimate the ...

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Many people, including Andrew Ng in his Deep Learning Specialization, emphasize the importance of domain knowledge and developing hand crafted features. Only then one can achieve significant improvements in performance. A. Ng clearly talks about how hand crafted features are nowadays looked down upon but in fact, are important. Fundamental concepts in signal/...

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One problem with an acoustic link is frequency dependent multi-path fading/reinforcement, which can vary widely as the source and mic positions change, or as the room acoustic vary (moving hard objects, etc.) So I might try a "click" that has a wide and known pattern of several non-harmonically related spectra, and check the Hamming distance between the ...

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Your problem is at this step. You're doing half of a shortcut, but not the other half: $$x_k = \frac{2A}{T} \int_{0}^{T/2} \frac{2t-T}{T} e^{-i2 \pi k f_0’ t }$$ Start with the Fourier series definition (with the notation tidied up): $$x_k = \frac{A}{T_0} \int_{-T_0/2}^{T_0/2} \frac{2t-T_0}{T_0} e^{-i2 \pi \frac{k}{T_0} t } dt$$ What you did with this ...

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This is one of the best problems to demonstrate Fourier Series properties, and specifically the time derivative property: $$\frac{d}{dt}x(t) \overset{FS}\longleftrightarrow j2\pi kf_0 X_k$$ Instead of computing the integral $$X_k=\frac{1}{T_0}\int_{T_0}x(t)e^{-j2\pi kf_0t}dt$$ which is time consuming, you can take the first derivative of your signal and ...

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Not a full solution but a few hints: Note that your function has an odd symmetry. Hence the even Fourier coefficients should be zero. They don't seem to be in your case and I think that's a consequence of how you integrate: you integrate from 0 to $T/2$ instead of $-T/2$ to $T/2$. If you did both halves, they would turn out with opposing signs and then ...

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In different applications, this parameter has different value that results optimum output. How I can find optimum smf value? What do the docs say the smooth function does? Write that down mathematically. As for any mathematical problem: you'll set up a formula for the "error" you're making (or a formula for the "goodness" you're achieving), and then you ...

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The following is what I believe to be an optimized approach for performance in the presence of additive white noise when no other information is known about quantity of pulses or their amplitude distributions, beyond that they are 100 or 200 us long rectangular pulses and repeat at the 1KHz and 1.4KHz rates. This can be even further improved if any other ...

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First, the original $x$ and reconstructed $\hat{x}$ signals have a peak amplitude around $0.35$. Their difference peaks above $0.40$. That happens between two time-shifted like-alike signals. Second, the difference seems to relate to the amplitude. Processing maybe be non-linear, and it could be interesting to look at relative differences like $2(x -\hat{x}... 1 "I totally understand the concept of Fourier transform" Lucky you if you really do. Some of us (me, in first place) don't (in totality). The Fourier transform (and its avatars) is a prototype for duality. Duality here means that you can represent a signal on some primal domain (time) onto a dual domain (here frequency). This transformation is meant to ... 2 To make it sound natural you typically introduce some small random pitch, speed & gain modulations. That's not a trivial amount of work, especially if you want something that sounds natural and good and maintains the original phrasing. This is a pretty common plug-in in audio processing. It's typically called "vocal doubler" or "voice doubler" and ... 0 In the discrete case, as when feeding a digitized signal to a DFT or FFT, each output point in the FFT spectrum is the magnitude output from a simple bandpass filter (a Goertzel filter result, or equivalent complex FIR filter). For a rectangular windowed FFT, each of those filters has a Sinc (or Dirichlet) shaped filter response. The more input signal ... 0 The magnitude of$X(\omega)$for a given$\omega$signifies how much does the signal$e^{j\omega t}$exist in the signal$x(t)$; indicated as an inner product between$x(t)$and$e^{j\omega t}$. 0 The magnitude of each bin is the magnitude of that frequency component for that waveform in the time-domain, specifically when the time domain waveform is expressed as a sum of complex exponential frequencies. In the frequency domain that includes positive and negative frequencies, each impulse for the Fourier Transform of an arbitrary waveform is the ... 1 There are various flavors physical interpretations of the continuous Fourier Transform. Here is the one that works best for me: The amplitude of the Fourier Transform is a metric of spectral density. If we assume that the unit's of the original time signal$x(t)$are Volts than the units of it's Fourier Transform$X(\omega)$will be Volts/Hertz or$V/Hz\$. ...

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To perform carrier recovery for FSK, if the data is random and can assumed to be equiprobable, then you can take the mean of the derivative of the phase versus time to determine the carrier offset. Optionally the phase change from one sample to the next can be estimated using using a complex conjugate product of successive samples (for small angles, the ...

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