Questions tagged [magnitude]

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26 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
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20 views

Interpreting FFT Phase - why phase of a cosine?

I understand how to interpret the magnitude result from the FFT, but why is the phase that we obtain, arctan(Im(x)/Re(x)) indicative of the phase shift of a cosine graph, and not a sine graph?
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74 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 ...
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2answers
127 views

Non-zero DFT components where zero is expected?

I am implementing DFT in Octave. Here's my code: ...
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56 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 ...
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109 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 ...
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1answer
94 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 ...
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1answer
3k 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 ...
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1answer
59 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 ...
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1answer
96 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 ...
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2answers
238 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: ...
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1answer
62 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 ...
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2answers
71 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 ...
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1answer
264 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 ...
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3answers
154 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 ...
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0answers
45 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 ...
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3answers
374 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 ...
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1answer
101 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 (...
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3answers
1k views

Understanding FFTs for simple Sin / Cos

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 reading this ...
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1answer
2k 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 ...
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3answers
77 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 ...
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43 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 ...
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1answer
264 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 ...
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57 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 ...
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1answer
233 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,...
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3answers
309 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. ...
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2answers
79 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: ...
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3answers
513 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 ...
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2answers
94 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)| &=\...
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1answer
105 views

Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$

I'm asked to sample the signal $$x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$$ with sampling frequency $F_s = 1000$ and plot the magnitude spectrum for the resulting sampled signal. My thinking is ...
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2answers
858 views

Zero padding and 2D Fourier transforms: how does zero-padding affect phase?

It's pretty clear that zero-padding an image before performing Fourier transform simply enlarges the magnitude image (stretching it to the new, padded size). What I can't understand is how it affects ...
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1answer
82 views

How would I find the function given the magnitude plot and the phase response?

I'm wondering how I'd find the Fourier Transform X(jw) given the following information: My understanding is that the expression for the continuous time fourier transform (CTFT) is magnitude(CTFT)exp(...
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2answers
194 views

How to graph magnitude plots for basic 4-pole filters?

I have developed magnitude plots for basic one-pole and two-pole filters derived from various Physics PDF's and tutorials I have found online and calculated from: https://www.desmos.com/calculator/...
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3answers
769 views

$e^{j\omega}$ on unit circle

I am new to DSP, and I'm self studying. I am confused about the magnitude of $e^{j\omega}$ - where $\omega$ is the normalized angular frequency - when we are on the unit circle. According to the ...
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1answer
143 views

Given a plot of both the magnitude $|H(\omega)|$ and its angle, How can you find the $H(\omega)$?

I'm specifically trying to use an inverse Fourier Transform to find $h(t)$, but I'm finding it difficult to get $H(\omega)$ in the first place. I'm under the impression from my textbook that $H(\...
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1answer
1k views

Spectrogram with square or non-square magnitude of STFT: power vs. magnitude

As seen in this question and answer, to do a spectrogram, it's common to plot either: the square magnitude $|\text{STFT}(\text{frame}, \text{bin})|^2$ ("power spectrum") the magnitude $|\text{STFT}(\...
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4answers
2k views

How do I calculate peak amplitude of the signal components after zero padding and FFT?

I am learning about DFT and trying to apply it to some audio processing. I am new to DSP but experienced in programming and have some background in math and physics. The FFT algorithm I use (lomontFFT)...
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1answer
274 views

Summing magnitudes of individual frequency bins

I am working on signal analyser and have problem with understanding relationship between display resolution and frequency resolution (range). My frequency range is $ 1-20000\quad [ H z ] $ so to ...
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1answer
140 views

Why harmonic components appear only after a certain level when a signal is clipped?

I recently observed this phenomenon that when a signal is clipped the harmonics start to appear only after a certain level. The Python code to reproduce the effect is given below. The signal has 3 ...
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2answers
225 views

Phase information from product of complex conjugate transfer functions

For an input signal $x(t)$ and output signal $y(t)$ through an LTI system I $H(t)$ I have found and interesting property that concerns signals' power spectral densities: $${\lvert H(\omega)\rvert}^2 =...
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1answer
62 views

Computing real signal with minimum absolute values from even magnitude spectrum

I want to derive a real audio signal from an arbitrary even magnitude spectrum. The phase spectrum affects the values of the signal in the time domain; for example, a phase of 0 for all frequencies ...
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1answer
1k views

Magnitude response and DFT normalization

Suppose I have an FIR denoted h that represents the impulse response of a system. Using MATLAB syntax (for convenience and brevity), What does ...
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1answer
316 views

Calculating phase response of maximum phase filter using Hilbert Transform

Given only a magnitude response $A(\omega)$ of a minimum phase filter, one can calculate the phase response using the Hilbert Transform: $$θ(ω) = -\mathcal{H}\{\ln(A(\omega)\}$$ This paper suggests ...
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2answers
8k views

Plotting the magnitude response of a filter?

I have designed a second order butterworth filter. Sampling frequency: $4\textrm{ kHz}$, Cut-off frequency: $500\textrm{ Hz}$ $$e = \tan⁡\left(\frac{\pi \times f_c}{f_s}\right) = \tan\left(\frac{...
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1answer
109 views

Does a filter need to completely attenuate high frequencies to be considered low-pass?

I'm looking at a system with a frequency response that is: $$H(e^{j\omega})=\tfrac{1}{4}(2\cos(\omega)+\cos(2\omega)+2)$$ I think the magnitude of this system looks like this (not sure what is the ...
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1answer
1k views

When does the Amplitude Spectrum equal the Magnitude Spectrum?

I had the following question on edX: I'm failing to understand why the second signal has $M(\omega)=A(\omega)$. First I find the DTFT of the signal: $$\mathcal{F}\{\delta [n]+\delta [n-1]\}\ =\ ...
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1answer
3k views

Magnitude of function in $z$ domain

I am newbie to $\mathcal Z$-transform, I searched to find the magnitude of a function in $z$-domain, but I couldn't find anything, for example when we have $$ H(z) = \frac{z-3}{z-0.5} $$ How do you ...
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1answer
920 views

How to reconstruct signal of its phase and magnitude functions?

I have two continuous periodic (a period of $2\pi$) functions which belong to the phase and magnitude of Fourier transform of a signal, how can I reconstruct the original signal? What kind of ...
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2answers
11k views

How does zero-padding affect the magnitude of the DFT?

Let's simulate sinusoids of two frequencies using the following Matlab code: ...
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1answer
933 views

Recovering signal from magnitude and phase of FFT

I'm trying to code the basics of an analysis-synthesis system on MATLAB, but I'm getting incorrect results. From the Wikipedia page: $$ X_k=\lvert X_k\rvert e^{i\angle X_k} $$ Here's a simple MATLAB ...