How I can plot the magnitude and phase response oh the function

i want do that for this function y=(4*sin(50*t)/(6*t)

Answer 1

[sixwwwwww]

Dear Helda, here is an example showing amplitude and phase plots of your defined function:

t = 1:100;
y = 4 * sin(50 * t) ./ (6 * t);
figure, plot(t, abs(y)), title('Amplitude plot')
figure, plot(t, angle(y)), title('Phase plot')

I hope it helps. Good luck!

[Helda]

thanx alot :)

[Helda]

oh ,,,, but i want to plot the response oh this function ,,, i think we will convert the function to frequency domain ,,, plz help me

[sixwwwwww]

You can do so by the following way:

syms t y s
y = 4 * sin(50 * t) / (6 * t);
figure, ezplot(abs(y), [1, 100]), title('Amplitude of transfer function'), ylabel('Amplitude')
figure, ezplot(angle(y), [1, 100]), title('Phase of transfer function'), ylabel('Phase')
response_function = laplace(y, t, s);
figure, ezplot(abs(response_function)), title('Amplitude of response function'), ylabel('Amplitude')
figure, ezplot(angle(response_function)), title('Phase of response function'), ylabel('Phase')

Good luck!

[Helda]

hi i want to ask u some question :) what the meaning of this code ?? fs=100; t=0:1/fs:5; x=4*cos(2*pi*10*t+pi/6); X=fft(x); n=length(x); c=(-1*fs)/2:fs/n:fs/2-fs/n; subplot(4, 1, 1),plot(t,x); subplot(4, 1 ,2),plot(c,fftshift(abs(X))); subplot(4, 1, 3),plot(c,phase(X)); subplot(4,1 ,4),plot(c,real(X)); ...... why did use this statement (( n=length(x);))?? i hope u can help me !!

[sixwwwwww]

Here is the explanation of this code:

fs = 100; % It is sampling frequency
t=0:1/fs:5; % It is time series used to generate signal x
x = 4 * cos(2 * pi * 10 * t + pi / 6); % x is function of t
X = fft(x); % This statement computes Fourier transform of x
n = length(x); % length(x) gives the array length of signal x
c = (-1 * fs) / 2:fs / n:fs / 2 - fs / n; % It generates the frequency series to plot X in frequency domain
subplot(4, 1, 1),plot(t,x); % This subplot shows the signal x vs. time series t
subplot(4, 1 ,2),plot(c,fftshift(abs(X))); % This subplot shows the Fourier spectrum of x with zero frequency component shifted to center
subplot(4, 1, 3),plot(c,phase(X)); % This subplot shows the phase distribution of X (Fourier transform of x)
subplot(4,1 ,4),plot(c,real(X)); % This subplot shows the real component of X spectrum

and the statement

n=length(x);

is used to make the length of frequency series equal to length of time series to plot Fourier transform of signal x correctly

[David]

Wow, way to make her put in a little effort of her own.

[Helda]

plz help me :/ for filter with a transfer function of H=(0.1667*s^3-0.5*s^2+0.5*s+0.1667)/(s^3-0.3333*s) what is the filter order ? what the filter type ? (FIR,IIR) why? plot the frequency response of the filter ? find the filter gain by matlab ?

[Engr Muhammad Amir Shahzad]

@sixwwww. Why you used *fftshift* in plotting magnitude of signal?

Answer 2

[David]

"How I can plot the magnitude and phase response of the function

 y=(4*sin(50*t)/(6*t)"

From what I've read, it seems you want the amplitude and phase of this function in the frequency domain. If this is the correct assumption to make, then you will need to make a lot more specifications. You will need to know your sampling rate, Fs, and either your time of observation or the number of points you have sampled. After you have figured these out, look into 'fft' function MATLAB provides.

An alternate route would be to use MATLAB's symbolic toolbox. You will want to look into how to create symbolic variables and symbolic equations as well as how to use the 'laplace', 'subs', and 'ezplot' functions. Good luck.

Answer 3

[Afshin Aghayan]

look at the following Matlab function, it can calculate phase spectrum as well as amplitude spectrum with a perfect accuracy:

https://www.mathworks.com/matlabcentral/fileexchange/63965-amplitude-and-phase-spectra-of-a-signal--fourier-transform-

This program calculates amplitude and phase spectra of an input signal with acceptable accuracy especially in the calculation of phase spectrum.The code does three main jobs for calculation amplitude and phase spectra. First of all, it extends the input signal to infinity; because for calculation Fourier transform(FT) (fft function in Matlab), we consider our signal is periodic with an infinite wavelength, the code creates a super_signal by putting original signal next to itself until the length of super_signal is around 1000000 samples, why did I choose 1000000 samples? Actually, it is just based on try and error!! For most signals that I have tried, a supper signal with 1000000 samples has the best output.

Second, for calculating fft in Matlab you can choose different resolutions, the Mathwork document and help use NFFT=2^nextpow2(length(signal)), it definitely isn't enough for one that wants high accuracy output. Here, I choose the resolution of NFFT=100000 that works for most signals.

Third, the code filters result of FT by thresholding, it is very important step! For calculating phase spectrum, its result is very noisy because of floating rounding off error, it causes during calculation "arctan" even small rounding off error produces significant noise in the result of phase spectrum, for suppressing this kind of noise you can define a threshold value. It means if amplitude of specific frequency is less than predefined threshold value (you must define it) it put zero instead of it.

These three steps help to improve the result of amplitude and phase spectra significantly.

IF YOU USE THIS PROGRAM IN YOUR RESEARCH, PLEASE CITE THE FOLLOWING PAPER:

Afshin Aghayan, Priyank Jaiswal, and Hamid Reza Siahkoohi (2016). "Seismic denoising using the redundant lifting scheme." GEOPHYSICS, 81(3), V249-V260. https://doi.org/10.1190/geo2015-0601.1

Answer 4

[Ammar Uddin]

How can I plot the magnitude and phase spectrum of this DTFT.

x(n) = a*n u(n)

Answer 5

[wyeen chow]

Hi, can i know how to plot a magnitude and phase spectrum for full wave rectifier? I had calculated manually?

Answer 6

[SRIKRISHNAN SRIRAMAN]

Consider a sinusoidal signal with frequency components of 5Khz, 12Khz and 14Khz .

Find and plot the magnitude and phase spectra of the signal.

Plz suggest me how

to code this question

Answer 7

[Gabriele Bunkheila]

Though some of the answers provided here may be literally correct, my sense is that the untold question is pointing to magnitude and phase of a Fourier decomposition. The short and simple example Discrete Fourier Transform may be more helpful in that respect.