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Discussion on the relationship between the FFT magnitude spectrum and the corresponding actual amplitude

This might be a bit long, but it's a question that has troubled me for a long time, and I hope to get everyone's help. When studying signals and systems, we usually only pay attention to the relative ...
lilili's user avatar
  • 11
1 vote
2 answers
100 views

Why in 2D Fourier Transform phase seems to be more "useful" than magnitude?

In 1D signals f(t) (e.g. a sound signal - independent variable t-->time) when we want to use informations from the Fourier transform F(ω) in order to reconstruct the signal, using the magnitude |F(...
user1198483's user avatar
0 votes
1 answer
53 views

Minimizing maximum instantaneous magnitude by applying phase shift

Suppose I have the following sum, where all the input variables are positive real numbers while the output is complex-valued data $$a e^{i \left( x + y \right)} + a e^{i \left( x - y \right)} + a b e^...
5-limit_JI's user avatar
1 vote
1 answer
62 views

Correction Factor for np.fft.rfft

I tested the function np.fft.rfft using the following code and determined the magnitude of a $50 \, \textrm{Hz}$ sine wave. ...
Tom's user avatar
  • 131
0 votes
1 answer
33 views

How to compute the direction/bearing of a vector time series in the frequency domain (i.e. as a function of frequency)?

I have a time-domain magnetic field, $\mathbf{b}(t)$, with components $b_x(t)$ and $b_y(t)$ where $x$ and $y$ denote orthogonal coordinate directions (i.e north and east, respectively). At each time, ...
Darcy's user avatar
  • 296
2 votes
3 answers
795 views

Why does spectrum magnitude decay away from DC for positive signals?

I would like to understand why the second frequency component usually has the greater magnitude within the range [1, (N/2)], i.e why (I remove the DC component and ...
Franck Might's user avatar
0 votes
1 answer
65 views

Magnitude spectrum of LTI system output signal

First year student so please excuse my lack of knowledge. As i understand i need to use convolution which is: $$ y^{out}(t) = u^{in}(t) * h(t) $$ Or maybe my thoughts are wrong so please correct me. ...
Illia Zakharov's user avatar
0 votes
4 answers
514 views

FIR filters: is it possible to manipulate phase without change in magnitude response

Here's response of FIR design: which shows SPL 0dB and here's a wave file exported from ( DRC ) FIR design software: FIR48kHz.wav. Audio software (internally uses FFTW routines) where this filter is ...
Juha P's user avatar
  • 917
0 votes
1 answer
112 views

What is discrete in value/amplitude/magnitude?

A digital signal is commonly described as a signal which is discrete both in time and value/amplitude/magnitude. I understand what is "discrete in time" (say, the signal is received each 1 ...
hamza's user avatar
  • 3
2 votes
1 answer
446 views

Understanding the multiply by 2 factor in scaling the DFT magnitude

I have seen a number of answers on various forums for why we need to scale the magnitude of DFT output by 2 (e.g. 1) to account for discarding negative frequencies, or 2) due to the 2 in the ...
Joseph's user avatar
  • 223
0 votes
1 answer
65 views

Why is DFT magnitude less than expected?

Code for signal: ...
Dmitry  Sokolov's user avatar
0 votes
2 answers
770 views

Why some FFT return complex array, some - mirrored real array?

I have 64 samples of a signal, two sines, one at 0.1 max freq, another at 0.5. Wrapped in gaussian: In my JS version of FFT I get an array of numbers, but the size is double (128 elements) and the ...
shal's user avatar
  • 111
2 votes
1 answer
1k views

Log Mel Spectrogram vs Log Mel Power Spectrogram

I'm doing some feature extraction on audio signals. $M$ being a mel filterbank matrix, and $S$ being the spectrogram (extracted from the Short Time Fourier Transform of my audio signal), we can ...
Jdip's user avatar
  • 6,300
2 votes
1 answer
247 views

Calculating transfer function for a comb filter with low-passed feedback

I'm creating a comb filter bank as part of a project I'm working on, and I need a way to visualize its magnitude response. The project already has FFT-based analyzers that can generate this response, ...
Jackson Kaplan's user avatar
3 votes
1 answer
91 views

Can we recover $|X(k)|$, given $|x(n)|$?

Given a complex vector $x[n]$, we can find the magnitudes of the spectrum by computing: $X_m[k] = |X[k]| = |FFT[x]|$ This involves performing a complex FFT and computing the absolute value of the ...
Logan's user avatar
  • 55
0 votes
1 answer
41 views

Different complex pairs giving same magnitude and phase

I am trying to fit data of magnitude and phase to get complex pairs(for FFT), but I think it would be a wrong approach as different pairs of complex numbers can give same amplitude and phase , is my ...
Novice_Developer's user avatar
0 votes
1 answer
194 views

How can I interpret the output of indexing an fft in python?

I am looking to determine whether a given audio file contains a certain frequency, similar to this question. However, as a beginner, I need help understanding the output. If I am understanding the ...
fishfinder's user avatar
0 votes
1 answer
412 views

Confusion understanding Fourier series line spectra?

I am reading book signals and systems Laboratory with MATLAB where I am studing chapter 5, Fourier series and i trying to understand magnitude spectrum and phase spectrum but i have certain confuisons ...
DSP_CS's user avatar
  • 1,880
1 vote
1 answer
274 views

Scaling of FFT2 magnitude in image-processing

I got the following code: ...
j35t3r's user avatar
  • 157
0 votes
2 answers
79 views

Computing magnitude response of system

Suppose I have this equation: $$H\left( e^{j\omega }\right) =\dfrac{1+e^{-j\omega }}{1-0.1e^{-j\omega }}$$ How do I find the magnitude exactly? I tried expanding it, but it seems to not work. $$\frac{...
Meep's user avatar
  • 109
0 votes
1 answer
651 views

Z domain Transfer function to magnitude

How would one go about calculating the Magnitude of... $\mathcal{Z}$-transform = $$\frac{1}{1-z^{-2}}$$ I understand that z can be replaced with $${exp}^{j\omega}$$ and I am aware of the identities $${...
New2Dsp's user avatar
-1 votes
1 answer
81 views

Draw the poles and zeros in the z plane for a system with poles at 0.45±j1.06 and zeros at 0.58±j2.06 Also plot the magnitude response of the system

Can you guys share 1 resource that solves similar type of this problem. This is not do my homework post. I just want a place which solves this type of problem. If you have pdf in book or sth, do share ...
achhainsan's user avatar
0 votes
0 answers
47 views

Stable and causal system

How many stable and causal systems with the same magnitude response are there? I know this relates to an all pass system for two rational transfer functions but am not sure about the specifics of this
Amanda Mironia's user avatar
1 vote
1 answer
195 views

Why do the DTFT and FFT give me completely different results for magnitude at a specific frequency?

I am trying to write a program to compute the magnitude and phase of a specific, non-integer frequency component (i.e. given a sampled finite signal of length $N$, I want to know the magnitude and ...
Tommy Wolfheart's user avatar
2 votes
2 answers
342 views

Non-zero DFT components where zero is expected?

I am implementing DFT in Octave. Here's my code: ...
Devashish Jaiswal's user avatar
0 votes
0 answers
89 views

Blackman window magnitude attenuation

I am trying to compute the fundamental phasor using sliding window DFT. I have employed a Blackman window in conjunction i.e $$ \sum_{k=0}^{L_{DFT}-1}x(k) w(k) e^{-j2\pi k/N} $$ where $x(k)$ is the ...
mka_07's user avatar
  • 15
0 votes
0 answers
457 views

Moving average filter output magnitude in simulink

I was using the Moving average filter provided by simulink. I set the window length equal to 31 samples and i was using a fixed step solver with a step size of $\frac{1}{(50\times24)}$. I used a unit ...
mka_07's user avatar
  • 15
-1 votes
1 answer
287 views

SMA, SVM and PSD python

I'm looking for python functions (package) to calculate SMA (signal magnitude area), SVM (signal vector magnitude) and PSD (Power Spectral Density). The goal is to extract features from an ...
Ziad's user avatar
  • 1
5 votes
1 answer
31k views

Calculate the magnitude and phase of a signal at a particular frequency in python

I have a signal for which I need to calculate the magnitude and phase at 200 Hz frequency only. I would like to use Fourier transform for it. I am very new to signal processing. And this is my first ...
thileepan's user avatar
  • 183
1 vote
1 answer
237 views

Magnitude response of mirrored (with respect to unit circle) poles and zeros

I just want to check that my understanding about the following paragraph from Optical Filter Design and Analysis by Christi K. Madsen, Jian H. Zhao is correct: A filter’s magnitude response is equal ...
Luis Gonzalez Guerrero's user avatar
1 vote
1 answer
659 views

Squared magnitude of the Z-transform

I am basically new to the $z$-transform and there are some points regarding its square magnitude that I do not understand. Basically I do not understand how in slide 4 of PDF, they arrive at the ...
Luis Gonzalez Guerrero's user avatar
0 votes
2 answers
3k views

How to convert magnitude to dB in matlab

I exported a diagram from FDTD simulation, and now I want to change the magnitude to dB, here is the exported codes: ...
Dong junkai's user avatar
1 vote
1 answer
122 views

Terminology for instantaneous phase of magnitude component of complex signal

In my field, we deal with data that are originally complex-valued. Typically, researchers convert their data from real + imaginary to magnitude + phase, and then discard the phase data (i.e., we ...
Taylor's user avatar
  • 13
0 votes
2 answers
139 views

Working with a sound's magnitude instead of amplitude

I'm working on a project, where we're recording sound with a piezo-disc which looks a little something like this: Now, unless we're doing something horribly horribly wrong, I've discovered that we're ...
madprogramer's user avatar
0 votes
1 answer
765 views

Impulse response from frequency response in Matlab

I am trying to design equalization filter and therefore I want to define my own amplitude and phase response and then to obtain the impulse response of the filter. I thought that the output of the ...
Deanna77's user avatar
1 vote
3 answers
163 views

What does this paragraph mean?

I'm reading this paper about about an algorithm to measure image sharpness, and am confused by these sentences in the 6th paragraph: It is well known that the attenuation of high-frequency content ...
Ivan's user avatar
  • 195
1 vote
0 answers
202 views

What is the "Energy" equivalent of the Magnitude Spectrum

I have a semantic issue regarding the discrete spectrum $X[k]$ of a time domain signal with limited length $x[n]$, so we're talking about the FFT. Now, when I what to compare the bandwidth and ...
ruhig brauner's user avatar
1 vote
3 answers
2k views

How do the magnitude and phase spectrum of an imaginary function look like?

Say I have the function $$x(t)=j \operatorname{rect}(t)$$ Is the phase spectrum even or odd? I am confused whether the phase spectrum is an odd/even function of $\omega$ (angular frequency, Fourier ...
Saurabh Jadon's user avatar
0 votes
1 answer
626 views

Why is there a negative in front of the phase response equation for this complex exponential?

first time on here! I'm working through "Digital Signal Processing using MATLAB" by Vinay and Proakis. Good book. I am stuck on this example tho. Shouldn't the imaginary part in the denominator (...
Dom's user avatar
  • 61
6 votes
3 answers
2k views

Understanding FFTs for simple Circular Function (sin/cos)

Background : This is my first question in this forum, and although I read several threads on this side and googled a lot I could not find the answer to my question (maybe it is too basic)? For anyone ...
Jonas Jo's user avatar
-1 votes
1 answer
5k views

Calculating the magnitude spectrum and phase spectrum

From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$. Then, I want to calculate its magnitude spectrum and phase spectrum. The ...
keanehui's user avatar
0 votes
3 answers
110 views

Relationship between DFT input sequence and magnitude

Assuming there is a sequence that could look like this: $$ x[n] = \{1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,1, 1, 0, 0, 1, 1, 0, 0,1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0\} $$ Using this sequence, I want to ...
P_Gate's user avatar
  • 113
0 votes
0 answers
58 views

FFT frequency-magnitude not correct when a positive gain EQ point is applied

I have a measurement system, which applies a log sine sweep as stimulus to a DUT and records the return signal. I then extract the impulse response, and perform an FFT on this to examing phase and ...
samp17's user avatar
  • 159
0 votes
1 answer
505 views

Correctly scaling FFT of different lengths

I have been looking at using two FFTs of different lengths and displaying the output magnitudes on the same graph (a shorter length window for the higher frequencies, and a longer one for lower ...
samp17's user avatar
  • 159
0 votes
0 answers
69 views

Magnitude attenuation by a filter

I have a filter, with coefficients given by $$ W=\sin((2*\pi*2*F_f*k/F_s)/(2*\pi*2*F_f*k/F_s))*h[k] $$, where $F_f$ is the filter reference frequency, $k$ runs from $-N/2$ to $N/2$ ($N$ is the order ...
mka_07's user avatar
  • 15
1 vote
1 answer
469 views

Energy definition for Autocorrelation lag 0 and lag 1 for complex signals

I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix. Consider a complex input signal $x(k)=[x1,x2]^T$ and $x(k-1)=[x0,...
chaosmind's user avatar
2 votes
3 answers
445 views

Matlab IIR cheby2 bandpass, problems with Magnitude

I am trying to implement an IIR bandpass in Matlab. There are two things I don't understand. But first of all, let me post the code. ...
user44791's user avatar
0 votes
2 answers
371 views

Is it valid to calculate the magnitude, power, and phase of a real time-domain signal without converting it to the frequency-domain?

I would assume you perform the calculations the same way, but since there would be no imaginary component because the signal is not complex it would be simpler: ...
tjwrona's user avatar
  • 327
2 votes
3 answers
909 views

Frequency response of a microphone using a sine sweep

I want to determine the frequency response (magnitude, phase) of a microphone. I have another "good" reference microphone whose frequency response I know. I understand that I can use a good speaker ...
Crenguta's user avatar
2 votes
2 answers
245 views

Phase response of $H(f)=e^{-j2{\pi}ft_0}$

Given is the impulse response: $$h(t)=\delta(t-t_0)$$. I calculated $$H(f)=e^{-j2 \pi ft_0}=|H(f)|\cdot e^{j\varphi(f)}$$. Now, the magnitude response of $H(f)$ is: $$\begin{align} |H(f)| &=\...
Zelda_CompSci's user avatar