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The answer is the same to the question: "Why do we need computers to process data when we have paper and pencil?" DTFT as well as the continuous-time Fourier Transform is a theoretical tool for infinitely long hypothetical signals. the DFT is to observe the spectrum of actual data that is finite in size.


12

TL, DR: world pervasive algorithms (FFT-related)! The continuous Fourier transform, the Discrete-time Fourier transform (DTFT) and the Discrete Fourier transform (DFT) share conceptually similar traits (regarding energy, convolution, shift, scale, etc.) The DFT unveiled a very scalable and fast algorithm to put those concepts into practice: the FFT. It is ...


3

I designed a lot of DSP algorithms and I would usually be the one implementing them in an FPGA. I rarely had to explain the internals of an algorithm to other people. That beind said, it is a good idea to represent the number of bits (I usually used the s:m:f notation from Sony Playstation 2) in a block diagram/design document for every components. You ...


2

Based on the blog post - The Paint Bucket in Paint.Net 4.0 (Video) I can tell it uses some edge detection to handle similar colors within a piece wise smooth area. More information is given in the Paint Bucket Tool documentation. Usually the way it can be implemented is by defining color metric. How far a color is form another color. If it within the ...


2

Reversing the order of the input sequence would provide the same result as what the OP achieved, but not to say this is exactly why it is occurring here. Below shows the details of the DIT algorithm after each stage; comparing each element step by step with the code should reveal the actual error. Interpreting the OP's results (I assume [x] represents the ...


2


2

Some of those notions can seem quite vague, and may even depend on the field. In algorithmics, different types of complexities come at play. One could be related to actual implementations (machine or computational complexity). Another to data access (sample, training set complexity). Computational complexity is generally machine-, transmission-, power ...


2

Since there is no prior at the Vector level this is basically element wise problem. Moreover, if we assume the noise to be White Noise with zero mean then the answer can be very simple. Since the phase difference is always a multiply of 180 [Deg] we can, without loss of generality, assume they are on the real axis. So what we have can be modeled as: $$ {z}_{...


2

I created a signal with two sinusoids and added increasing amounts of random noise to it. The results of running the FFT and MUSIC on this signal are shown in the image below. You are using pmusic(). MUSIC (MUltiple SIgnal Classification) is a general algorithm that can estimate all kinds of parameters out of a signal. pmusic() is a MATLAB function that ...


1

The output of an FIR filter is $$ y(n) = \sum_{i=0}^{N-1}w_i(n)x(n-i) $$ Say the weight vector $\mathbf{w}(n)$ has a length of $N$, i.e., $$\mathbf{w}(n) = [w_0(n), w_1(n), \ldots, w_{N-1}(n)]^T$$ and the input vector $\mathbf{x}(n)$ should have the same length as $\mathbf{w}(n)$: $$\mathbf{x}(n) = [x(n), x(n-1), \ldots, x(n-N+1)]^T$$ Therefore the output $y(...


1

Judging from your description alone, I'd say an algorithm to find appropriate 3-clusters of timestamps would be something like: compare the three first elements of your sorted lists. Pick the earliest of the three. Remove the element from its list. determine difference of that element to the other two first If both difference are below a "simultaneity&...


1

However, if we can detect the start of the packets, we should be able to find the start of the data symbol since the length of the preamble is known at the receiver, so why would we use still employ the symbol timing estimation algorithm to find the start of the data symbol. The start of packet detection isn't accurate enough. When you look into the ...


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 can use the Infinite Series to compute arctan, then you can use arctan & sqrt to compute arcsin. Note: edge-cases not intercepted - might explode at the points of discontinuity, aka divZero. public MyRational Arctan() { // https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Infinite_series MyRational sum = new MyRational(0); ...


1

In one level DWT, each output of the low-pass or a high-pass can indeed be considered as signals. Thus each of those signals are subsampled by a factor of 2, and the same two-filter-subsampling is iterated on the low-pass output, several times (wavelet decomposition) at $L$ levels. Each final output of the different branches could still individually be ...


1

Here is one answer, if someone can improve on this I will select it as the "right" answer (also comments very welcome on obvious flaws with this approach): Given Cauchy's argument principle, the number of zeros outside the unit circle is given by the number of encirclements of the origin for the frequency response of the filter as plotted on a complex plane....


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