# Tag Info

Accepted

• 90.5k

### 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 ...
• 331

### 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 ...
Accepted

### 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 ...
• 90.5k
Accepted

### 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 ...

### 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 ...
• 90.5k
Accepted

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 ...
Accepted

### 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 ...
• 4,583

### 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 ...
• 90.5k
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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 ...
• 4,295
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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, ...
• 35.4k
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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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• 90.5k
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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. ...
• 28.3k
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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, ...
• 9,004
Accepted

### involutory transformations - why are they not so much used in signal processing?

You don't chose transforms by whether they are involutions or not. If invertibility is of interest, any simple form of inverse is sufficient. Useful transforms reveal structure of some sort or ...
• 4,583
The answer to this question is yes. There exist a fast triangle transform, FTT, for triangle waves which has a complexity of $N\log_2(N)$, where $N$ is the number of elements. It works the same like ...