# Tag Info

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### IIR Hilbert Transformer

This is achievable with two parallel all pass filters. The two all pass filters synthesize an odd ordered low pass filter whose pass band extends from -90º to +90º in the z-domain. (I will discuss ...

### IIR Hilbert Transformer

I have insufficient reputation to answer in the comments, so here goes: I believe Olli calculated his coefficients using some kind of genetic algorithm (I don't know the details). All I did was plot ...
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### Hilbert transform too large to store (out of core processing)

I would use a linear phase FIR Hilbert transformer, and use block processing, such as the overlap-add method. That means that you partition the input signal into contiguous non-overlapping blocks and ...
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### FFT equivalent for generalized unitary transforms

It's all about structure. One early paper on this is A Unified Treatment of Discrete Fast Unitary Transforms, 1977: A set of recursive rules which generate unitary transforms with a fast ...
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### Time domain maximum from frequency domain data?

Suppose that Alice has a vector $\mathrm x \in \mathbb R^n$. She computes the DFT of $\mathrm x$ $$\mathrm y := \mathrm F \mathrm x \in \mathbb C^n$$ where $\mathrm F \in \mathbb C^{n \times n}$ is a ...

### Fourier Transform of a signal using direct integration and properties

Your first solution using the properties of the Fourier transform is correct. Your second solution is wrong, because you forgot to include the unit step function. Your function $g(t)$ should be ...

### Finding Laplace Transform without ROC

Strictly speaking you can't because without specifying the ROC, the inverse Laplace transform is generally not unique. However, in many contexts there is the implicit assumption of causality of the ...
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### Fourier Transform of exponential

The plot is of $$\mid X\left(i\omega\right) \mid = \sqrt{\left(\frac{1}{a+j\omega}\right)\left(\frac{1}{a-j\omega}\right)} = \frac{1}{\sqrt{a^2 + \omega^2}}$$ against $\omega$ In particular $\omega$...
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### Daubechies wavelet transform

Looks like you need a general explanation of the discrete wavelet transform (DWT). DWT breaks a signal down into subbands distributed evenly in a logarithmic frequency scale, each subband sampled at a ...

### Can anyone explain how does CZT (Chirp Z Transform) really help in 'spectral zooming'?

The CZT allows for a fairly general evaluation of the Z transform - the more general evaluation path looks like a spiral, so it has a radial component step size as well an angular step size.For ...
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### Useful natural "Hilbert-like" $n$-uples and $n$-fold "analytic signals

The generalisation of the concept of an analytic signal is not straight forward. I'm quite certain however that looking for such a generalisation with quarternions (or even octonions) will not turn ...

### When doing a Hilbert-transformation, why not simply multiplying by an exponential?

In contrast to Jason R's answer I claim that the Hilbert transform is a phase shift by $-\pi/2$ for real-valued signals. By definition, a phase shifter shifts the phase of a sinusoidal signal by some ...
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### How to sketch the following discrete-time signal?

I give you some hints and then you can solve this homework. Your $x[n]$ has only $8$ nonzero values. Figuring out what happens to them (in an exhaustive way) is not difficult. Consider $(n-1)^2$ and ...
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### Conditions for which the Hilbert transform returns a correct phase

A single instantaneous phase estimate may or may not make any sense if there is more than one frequency peak in the signal's local spectrum. So, to get a better single frequency and phase estimate, ...
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### What is the difference between Constant-Q Transform and Wavelet Transform and which is better

A Constant Q transform is a variation on the DFT. In other words, it is a type of wavelet transform. I only have a casual understanding of both types of transforms myself, so take what I'm saying with ...
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Note that the antiderivative of a function is only defined up to a constant. Furthermore, note that if you integrate a periodic function, the result is not necessarily periodic. Let $$x(t)=\sum_{k=-\... 4 votes ### Is there an easy way to translate a Fourier transform table from angular frequency \omega to Hertz f? Your confusion comes from the fact that you use X(\cdot) for denoting both functions, the function of \omega and the function of f, but they are really two different functions, because$$X(\...
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TLDR: if the time variable $t$, and its dual variable ($f$, $\tau$) in the expression of the bivariate kernel have the same homogeneity, (I believe that) you can call it a time-domain ...
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### 1D DCT matlab code

You have mistyped the formula, replace this line sum = sum + y(i).*(cos((pi.*(2.*y(i)+1).*u(j))/(2*N))); with the one below, and it works fine. ...
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### How to alleviate the edging effect of the Hilbert transform?

The effect can be alleviated with appropriate padding, which imposes a 'statistical prior' (i.e. assumption). No padding is equivalent to periodic padding$^{1}$, meaning signal's right joins its left, ...

### Can anyone explain how does CZT (Chirp Z Transform) really help in 'spectral zooming'?

This part of that paper suggests the answer: The issue being that the standard FFT just does linearly-spaced spectral samples from $-f_s/2$ to $f_s/2$ where $f_s$ is the sampling frequency. The CZT ...
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### Is DCT (Discrete Cosine Transform) of Type-2 lossless or lossy?

Mostly yes, but it depends on the context. Let us elaborate. DCT-II is one of the many forms of Discrete Cosine Transforms, and probably the most widely used one, as it is (somehow) present in JPEG ...
The unilateral Laplace transform is used for analyzing causal linear time-invariant systems, which have an impulse response $h(t)$ that is zero for $t<0$. The unilateral Laplace transform can be ...