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9 votes

Factor $|a|^{-1/2}$ in definition of mother wavelets

My answer is for real scale $a$ and the fact that wavelet transform is usually defined in $L_2$ with norm $$||\Psi(\tau)|| = \int_\mathbb{R} \Psi(\tau)\Psi^*(\tau)\mathrm{d}\tau $$ So $$||\Psi_{a,t}...
AlexTP's user avatar
  • 6,605
6 votes

FIR filter Gain of 0dB at Passband Frequency

FIR coefficients are $h[n]$, the same as the impulse response. there are $N$ non-zero taps. $$ h[n] = 0 \qquad \text{for } n<0, n \ge N $$ frequency response is $$\begin{align} H(e^{j \omega}) &...
robert bristow-johnson's user avatar
5 votes
Accepted

Am I supposed to normalize FFT in Python?

Your decision to normalize or not does not change the accuracy of your answer, as it is simply a scaling factor. If you use the common scaling of $1/N$, then the output for each DFT bin will represent ...
Dan Boschen's user avatar
  • 52.9k
5 votes
Accepted

Is it possible to normalize FIR filter coefficients to "perserve gain on average"?

I'm wondering if there is a standard way to normalize its filter coefficient in a way to make the filter "energy preserving on average". If the filter isn't all-pass, then there wouldn't be ...
TimWescott's user avatar
  • 12.9k
4 votes
Accepted

How to choose the "best" measurment (from a given set) as input for a kalman filter?

Question: Which parameter is suitable to indicate how "good" the measurement fits to the Kalman filter? To estimate a quality of association you can use likelihood function. The likelihood ...
Gluttton's user avatar
  • 388
4 votes
Accepted

Overlap/add time-domain audio frames: How does normalization/scaling work with overlap greater than 50%?

Let's assume continuous time (rather than discrete time). If you do not process the windowed data at all, you would like the output (the sum of the windowed frames) to be equal to the original signal....
Olli Niemitalo's user avatar
4 votes
Accepted

What is the relationship between angular frequency and normalized angular frequency

Again there is no wrong or right here. In the Alan Oppenheim's Discrete-Time Signal Processing book, the notation is as follows: when there are only continuous-time signals we use $\omega$ for ...
Fat32's user avatar
  • 28.3k
3 votes
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How do I normalize a predesigned IIR filter?

As mentioned in the comments, you have to choose a frequency $\omega_0$ at which you want to normalize the gain. This could be DC (i.e., $\omega_0=0$) or any other frequency, depending on the filter's ...
Matt L.'s user avatar
  • 90.6k
3 votes
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Design a filter which passes all frequencies except $\omega=\pm\frac{\pi}{2}$ and plot its pole-zero diagram

The kind of filter you are looking for is a notch filter. Using filter design toolbox in Matlab you can get it as I'm showing you in the following picture: This has to be done in z-plane so there ...
VMMF's user avatar
  • 1,142
3 votes
Accepted

Signal normalization

[EDIT] After a second read, the proposed normalization looks non standard. Suppose that $m\le x \le M$ ($m$ and $M$ denote the min and max). The scaling factor will be, depending on the situation: if ...
Laurent Duval's user avatar
3 votes

Dynamic range compression - Need pseudo algorithm for normalizing a signal

from your posted waveform, i am assuming that this is a unipolar signal. that is $$ x[n] \ge 0 $$ in audio, it would be the same, except that we would be working on $|x[n]|$ instead. so first you ...
robert bristow-johnson's user avatar
3 votes
Accepted

How to normalize the FFT?

It's not clear how you are wanting to normalize the function. If you are wanting to normalize the spectrum so that the amplitude of the function in the time domain matches the amplitude of the ...
Baddioes's user avatar
  • 1,135
2 votes
Accepted

Obtaining normalized matrix for the Haar Wavelet Transform

After a few quick calculations, it seems to me that the trouble comes from poor notations for the root in your reference. If you read, in the final normalized matrix, $\sqrt{8/64}$ and $\sqrt{2/4}$ ...
Laurent Duval's user avatar
2 votes

Dynamic range compression - Need pseudo algorithm for normalizing a signal

here's an efficient sliding maximum algorithm that has cost that is $O(\log_2(L))$. below window_width is $L$. comes from Brookes: "Algorithms for Max and Min ...
robert bristow-johnson's user avatar
2 votes
Accepted

normalized sum of squared differences

In an attempt to solve the question on why to normalize, and implicitly how to normalize: $F$ is your reference patch, $I$ is the patch under inspection. So make $I$ only consist of the maximum ...
Marcus Müller's user avatar
2 votes

Factor $|a|^{-1/2}$ in definition of mother wavelets

Wavelets play differents role in functional spaces, especially as unconditional bases (see What are unconditional bases and which wavelets have this property?). In $L_p$ spaces, if $|\psi|^p$ is ...
Laurent Duval's user avatar
2 votes

The concept of normalized frequency

Consider a continuous signal $$ x(t) = \sin ( 2\pi f t) \ $$ of which we have the following measurent points: $$x_n = x(n T_s) = \sin \bigg(2\pi \frac{f}{f_s} n \bigg) \ . $$ We note that $\frac{f}{...
Mussé Redi's user avatar
2 votes

Normalization of a signal with respect to another signal

I have had the same problem. My signals are coming from the MRI machine. In my case, the scaling is one of my options; in a way, I divided the signal A and B to the maximum of signal A, but I could ...
Amir Shamaee's user avatar
2 votes

MFCCs and mean normalization

Why did he add the epsilon value 1e-8 This is so you don't end up taking log of zero later, although since the first operation isn't guaranteed to be >=0, I'm not sure if it's necessary or helpful
Alex E's user avatar
  • 21
2 votes
Accepted

Normalization factor in the convolution theorem

The choice of the normalization factor is just a matter of convention. Note that the specific correspondence between convolution in the time domain and multiplication in the frequency domain with a ...
Matt L.'s user avatar
  • 90.6k
2 votes
Accepted

Why is scaling of images / pixels into `[0, 1]` range performed before SIFT (Scale Invariant Feature Transform) algorithm?

Scaling images into the [0, 1] range makes many operations more natural when using images. It also normalizes hyper parameters such as threshold independently of ...
Royi's user avatar
  • 20.1k
2 votes

How to normalize the FFT?

You should look at this answer for more detail, but I'll summarize it here for you: Denote by $|X|^2$ the frequency averaged Squared Magnitude Spectrum and $w$ the window applied. The PSD is: $$\frac{...
Jdip's user avatar
  • 6,394
1 vote

Am I supposed to normalize FFT in Python?

Whether you want to normalize or not depends on whether you want to know the level or the energy of the DFT input. IIRC, the SciPy FFT returns energy (complies with Parseval’s relation). A signal N ...
hotpaw2's user avatar
  • 35.5k
1 vote

Autocorrelation - Understanding reduced correlation at periodic time shifts using np.correlate (versus statistical autocorrelation)?

The difference here is that statistical autocorrelation assumes a stationary power signal (so basically an infinite periodic signal) and does a normalisation to $[-1,1]$ and that autocorrelation just ...
Max's user avatar
  • 2,383
1 vote
Accepted

Why do we use normalized angular frequency?

We use normalized frequency units in DSP mainly for convenience-- most DSP textbooks are written this way so that the theory can be presented in terms of essentially unitless quantities. For ...
Robert L.'s user avatar
  • 2,222
1 vote
Accepted

why multiply grayscale images by 256

Grayscale images are typically stored as 8 bits per pixel in files. Perhaps the network was trained to work with such data. $2^8 = 256,$ so 8 bits can represent any number from 0 to 255. It may well ...
Olli Niemitalo's user avatar
1 vote

Normalization of a signal with respect to another signal

I think I understand what Vasilis is after with this question, so I will attempt to clarify for all, and answer. Let x(0...N-1) be a predetermined reference signal. Let y(0...N-1) be another signal. ...
kevin_o's user avatar
  • 11
1 vote

Making audio clips comparable in terms of RMS

I wrote this simple Matlab function a while back, it operates on dBFS: ...
742617000027's user avatar
1 vote
Accepted

Normalizing audio waveforms code implementation (Peak, RMS)

What is the best method to solve this? Intuitively, it seems I might need to calculate a local max or average based on a moving window (rather than the entire set) but I'm not entirely sure. Help? ...
A_A's user avatar
  • 10.7k

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