12

Does cubic interpolation (or any other) have any advantages over linear for the specific case of audio? You'd use neither for audio. The reason is simple: The signal models you typically assume for audio signals are very "Fourier-y", to say, they assume that sound is composed of weighted harmonic oscillations, and bandlimited in its nature. Neither linear ...


5

Audio signals An audio special-purpose analog-to-digital converter (ADC) normally has an internal or external analog low-pass filter and samples the analog filtered signal at a multiple of the target sampling frequency. This high-rate digital signal is then low-pass filtered by a digital decimation filter and decimated to the final sampling frequency. If we ...


4

Standard Savitzky-Golay filters are linear phase (type I) FIR filters. So they have an odd number of filter coefficients $2N+1$, and the delay equals $N$. For a good overview of Savitzky-Golay filters see this article by Ronald Schafer. For the definition of the four types of linear phase FIR filters see this answer.


3

Yes. The FIR filter model you're used to is a series of Neurons with weighted inputs, and a linear activation function. In other words, a standard FIR filter is a neural network. I mean, it's called "CNN". The C is exactly the operation a filter does.


3

Your 2-mic array can provide an angle-of-arrival estimate with front-back ambiguity, using cross-correlation to estimate TDOA and then calculating AOA from TDOA and microphone spacing. The front-back ambiguity can be removed with sufficiently directional microphones, or just by constraining the geometry, putting the microphones against walls, for example. ...


3

Part of your misunderstanding comes from the fact that there are many ways in which the radar signal processing chain is implemented. Depending on the type of radar, targets of interest, hardware, etc., some methods are more appropriate than others. We will consider pulsed-Doppler radar here. In the chain you describe: In modern pulse-Doppler systems using ...


3

Sorry MM, I'm agreeing with Havakok on this one: A time domain interpolation solution should do just as well, practically speaking, and be significantly cheaper in terms of computation. (Assuming most frequency content is a ways below Nyquist). I would go with cubic interpolation so you don't have any "corners" at the original sample points, which are of ...


3

My first swing at the answer had some very incorrect claims. I do not have access to the article, so I am inferring some things from the portion posted in the question. NOTA BENE: My arguments assume that the eigenvectors of $\mathbf{R}$ are arranged so that the first $n$ belong to the signal subspace and that the last $m-n$ belong to the noise subspace. ...


2

I've not worked on the design of such systems before, but I think your notions are on the money. Specifically, yes, beamforming arrays do have RF front ends that are replicated many times. The complexity of contemporary phased array radars is astounding in this regard; there are designs that have hundreds of individual antenna elements in them with ...


2

Depending on the window function, you may be able to use a DFT-even version of the window function. "DFT-even" means that the periodic extension of the window function is symmetrical. In MATLAB and Octave you can get such a window like this (the first line in the source code): a = hanning(10, "periodic"); b = fftshift(a); c = a + b; plot(...


1

I'm going to group number 1 and 3 as related. For a high level description of MUSIC, you can take a look at MATLAB's overview here. One of the main steps in the algorithm is to find the eigenvectors of a correlation matrix, which can be done via singular value decomposition or other methods. MATLAB has functions for this, so you may want to find equivalent ...


1

You must be assuming you have a dominant peak at zero from only looking at the same graph you shared, but if you really did remove the mean, then value at bin 0 will be 0 (as bin 0 is directly proportional to the mean). Inspect the data carefully as their does not appear to be anything wrong with the code with respect to the FFT. What is likely occurring is ...


1

Are you using scipy by any chance ? If yes , this might help https://scikit-dsp-comm.readthedocs.io/en/latest/_modules/sk_dsp_comm/digitalcom.html check for functions "QPSK_tx" and "QPSK_bb"


1

As far as I can tell from the graph, the variance of the signal goes up substantially under "oscillation" conditions. So, monitor the variance over a rolling window. High variance indicates oscillation. To choose the window width, consider: if the window is too short, the computed variance will be too noisy if the window is too long, the monitor will be ...


1

Arbitrary shapes is A LOT more difficult than rectangular rooms. You either need to do image method with visibility checking or some sort of ray, particle or cone tracing algorithm. There are few commercial programs that do this (Ease, Odeon, Bose Modeller, etc. ) and I doubt you'll find a free one. In addition the much more complicated algorithms, these ...


1

The order of the sound field indicates that there are constraints placed upon the sound field. In this context, the order equals that of the lowest-order Ambisonics multi-channel format that can describe the sound field. Ambisonics channels are weighted by directional patterns that are orthogonal spherical harmonics: Figure 1. Directional patterns of ...


1

First, I do not find any information on what is the order of the sound field. Can anyone elaborate please? $Y_{lm}(\Omega)$ is the spherical harmonics with mode $m$, order $l$ and frequency $\Omega=(\theta,\phi)$ (dictating angles of arrival, ex: azimuth, spherical, elevation, etc.). According to [1], we have the following formula: $$Y_{lm}(\Omega) = \...


1

First, we define $h_3[n] = h_2[n] \star h_2[n] = [1, 2, 1]$. From this result, we know that $h_1[n]$ must have 5 elements (so that $h[n]$ ends up with 7 elements). Let's define $h_1[n] = [g_1, g_2, g_3, g_4, g_5]$. We can find these as follows, using the definition of discrete convolution. First, we know that $g_1 h_3[0] = h[0] = 1$, so $g_1 = 1$. Then, ...


1

I'm posting this as a separate answer since my other answer has gotten so long and this is tangentially related. I translated Olli's Hermite code into Gambas. Besides the syntax differences, there is also a conversion from one-based arrays to zero-based arrays. I also took the liberty of precalculating some constant expressions (e.g. 1 / 2.0 ==> 0.5), ...


1

I don't know what the fuss is about. This is a simple vector problem. "Well, if it is that easy please elaborate. I have 4 microphones on the following locations (0.042,45,35),(0.042,-45,-35),(0.042,135,-35),(0.042,-1355,35). These are coordinates for the microphones with m1=(ri,θi,φi), where −π≤θ≤π and −π2≤φ≤π2. create a beam towards a sourse at (θs,φs)=(...


1

okay - I think the technique I was looking for is formulation of a synthetic aperture as in Synthetic Aperture Radar (SAR). The 'trick', in the general case, where static target and radar platforms are involved, would probably be that all the array elements will be physically present as opposed to conventional SAR where platform motion is used to synthesize ...


1

Just do a cross correlation with cc = scipy.signal.correlate(original,filtered) By position of the maximum, you can find out the filter delay. Just notice that the result will have length $2N-1$ with $N$ being the length of the original signal. So the delay in samples will be numpy.argmax(cc) -len(original)


1

You asked "how" without first asking "if", and, if so, under what circumstances. If you add two completely unknown numbers A + B and get 100, can you un-mix the sum to the original two numbers A and B? But if you know B = 7, you might have a solution. In the receiver case, if you know the 2 spectrums are disjoint (or other properties, such as redundancy ...


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