Im new to matlab and as part of my university assignment,im supposed to draw up these signals on matlab.and i have some problems regarding the units of the psd plots.
1)j=0:1/100:1; %time index
z=sin(2*pi*5*j); %sine wave signal
z=z*2;
plot(z),xlabel('Sampling Points'),ylabe;('Amplitude');
figure,psd(z)
2)noise=rand(1,100);
plot(noise);
figure,psd(noise);
3)[B,A]=butter(10,3/50,'low');
LPFz=filtfilt(B,A,z);
plot(LPFz)
figure,psd(LPFz)
4)y=wavread('sp1.wav');
Fs=44100; %sampling frequency
wavplay(y,Fs);
save sp1.mat y
plot(y(:,1)),title('Waveform of Speech'),xlabel('Sample Points'),ylabel('Amplitude')
figure,psd(y(:,1))
i would be extremely grateful to anyone who can help my by telling me the units i should use for the x axis of the psd spectrum,y axis is in dB ,that i got.i dont know what to out for x
If you are looking at your first example the x coordinate of plot (z) should be time. After all you define j as a time index and generate your z-function to be a function z(t).
If I am not mistaken your z function is a sine of structure 2*pi*omega*time with omega beeing a constant (5).
If u have further information about that constant you can be more specific about your x-axis.
As a matter of fact you can just look at your function: exponents as well as triangular functions (sine, cosine ,etc) have to be without dimension (seconds, meters ,kg, and so on)
If you were wondering about the units for the psd function, it is a spectrum. This means the x-axis is a frequency domain(1/seconds = 1Hz). In Matlab 8.2 it is recommended to use spectrum(z) instead of psd(z)
Related
I am currently working on a project for my Speech Processing course and have just finished making a time waveform plot as well as both wide/narrow band spectrograms for a spoken word in Spanish (aire).
The next part of the project is as follows:
Make a 3-D plot of each word signal, as a function of time, frequency and power spectral density. The analysis time step should be 20ms, and power density should be computed using a 75%-overlapped Hamming window and the FFT. Choose a viewing angle that best highlights the signal features as they change in time and frequency.
I was hoping that someone can offer me some guidance as to how to begin doing this part. I have started by looking here under the Spectrogram and Instantaneous Frequency heading but was unsure of how to add PSD to the script.
Thanks
I am going to give you an example.
I am going to generate a linear chirp signal.
Fs = 1000;
t = 0:1/Fs:2;
y = chirp(t,100,2,300,'linear');
And then, I am going to define number of fft and hamming window.
nfft=128;
win=hamming(nfft);
And then I am going to define length of overlap, 75% of nfft.
nOvl=nfft*0.75;
And then, I am performing STFT by using spectrogram function.
[s,f,t,pxx] = spectrogram(y,win,nOvl,nfft,Fs,'psd');
'y' is time signal, 'win' is defined hamming window, 'nOvl' is number of overlap, 'nfft' is number of fft, 'Fs' is sampling frequency, and 'psd' makes the result,pxx, as power spectral density.
Finally, I am going to plot the 'pxx' by using waterfall graph.
waterfall(f,t,pxx')
xlabel('frequency(Hz)')
ylabel('time(sec)')
zlabel('PSD')
The length of FFT, corresponding to 20ms, depends on sampling frequency of your signal.
EDIT : In plotting waterfall graph, I transposed pxx to change t and f axis.
Good evening guys,
I wanna ask you a question regarding the analysis of a function in the domain of frequencies (Fourier). I have two vectors: one containing 7700 values for pressure, and the other one containing 7700 values (same number) for time.
For example, I call the firt vector "a" and the second one "b". With the command "figure(1),plot(a,b)" I obtain the curve in the domain of time.
How can I do to plot this curve in the domain of frequency, to make Fourier transform?
I've read about the function "fft", but I've not understood very well how it can be used...can anyone help me?
Thanks in advance for your attention!
fft returns spectrum as complex numbers. In order to analyze it you have to use its absolute value or phase. In general, it should look like this (let's assume that t is vector containing time and y is the one with actual signal, N is the number of samples):
fY = fft(y) / (N/2) % scale it to amplitude, typically by N/2
amp_fY = abs(fY)
phs_fY = angle(fY)
Additionally, it would be nice to have FFT with known frequency resolution. For that, you need sampling period/frequency. Let's call that frequency fs:
fs = 1/(t(1) - t(0))
and the vector of frequencies for FFT (F)
should be:
F = (0:fs/N:(N-1)*fs/N)
and finally plots:
plot(F, amp_fY)
% or plot(F, phs_fy) according to what you need
I you can use stem instead of plot to get some other type of chart.
Note that the DC component (the average value) will be doubled on the plot.
Hope it helps
It's my first time performing an FFT within MatLab by experimenting with some example code from the MathWorks website. I was wondering if it was possible to take the code I have and transform the x axis to a log-scale representation rather than linear. I understand most of the code, but it is the x axis line of code that I'm still not 100% sure exactly what it is doing apart from the +1 at the end of the line, which is that fact that MatLab's indexing structure doesn't start on 0.
My code so far is:
[y,fs] = wavread('Wav/800Hz_2sec.wav');
NFFT = 4096;
Y = fft(y,NFFT)/length(y);
f = fs/2*linspace(0,1,NFFT/2+1);
plot(f,2*abs(Y(1:NFFT/2+1))
frequency usually comes out in linear scale from Discrete Fourier Transform. if you want, you can make a new frequency vector in log scale and interpolate the results you already have
fnew=fs/2.*logspace(log10(fs/length(y)),0,npts);
Ynew= interp1(f,Y(1:NFFT/2+1),fnew);
where npts is the length of your new frequency vector. for just plotting
loglog(f,2*abs(Y(1:NFFT/2+1));
honestly IMO, the interpolation thing doesn't work very well because FFT of real signals produces strong peaks and troughs in spectra, so unless you smooth your spectrum first, the interpolated spectrum won't look as nice
So I plot sine(w*time) vs cosine(w*time)
w being angular frequency.
Hope I'm not wasting anyone's time if I ask:
Would this look like a circle?
I've researched a whole bunch but most websites only graph sine and cosine side-by-side and show comparisons.
I got it to look like a circle and I was just wondering if this is correct.
Also, What can I call this plot? I just gave it a title "plot of a circle". But I am wondering if that is professional enough since I am doing it for class.
Thanks for your time and answers. Greatly appreciated.
My MATLAB code for anyone interested:
clear all; clc; % clear the Workspace and the Command Window
f = 2; w = 2*pi*f; % specify a frequency in Hz and convert to rad/sec
T = 0.01; % specify a time increment
time = 0 : T : 0.5; % specify a vector of time points
x = sin(w*time); % evaluate the sine function for each element of the vector time
y = cos(w*time);
plot(x,y)
axis equal
grid on
xlabel('sin(w*time)');ylabel('cos(w*time)');title('Plot of a Circle');
axis([-1.1 1.1 -1.1 1.1]);
print
Here is a link to a Wolfram Alpha query I just did:
http://www.wolframalpha.com/input/?i=x%3Dsin%28t%29%2C+y%3Dcos%28t%29
I am not sure if it what you want to see, but that site (WolframAlpha.com) is a great place to explore and challenge mathematical concepts that are new to you.
Also, I would call it a plot of a circle since that is what the output looks like.
You are making a Lissajous curve. Keep in mind that a cosine is just a sine offset by pi/2 radians, and so plotting a sine against a cosine will indeed result in a circle. Changing the frequency and/or relative phase between x(t) and y(t) will result in many different interesting patterns.
Consider the following script that plots a sine wave.
t = 0:pi/100:2*pi;
y = sin(t);
plot(t,y)
grid on % Turn on grid lines for this plot
This gives me a plot of sine wave. I understand the sine wave that appears continuous, should actually be discrete (my PC cannot store infinite no. of samples of continuous signal), and the matlab plot function does some kind of interpolation to connect the dots.
So In fact I also used stem instead of plot to see the sampled values (on time axis) of sine.
Now my question is there must be some sampling frequency used here. How much is that?
The sampling interval is the time interval between two consecutive samples of your signal.
The sampling frequency means how much samples of your signal you have in a fixed time interval, and it is reciprocal to the sampling interval.
You declared:
t = 0:pi/100:2*pi;
So your sampling interval is π/100. This means that your sampling frequency is 100/π.
If you want exact units, you'll have to determine the time units for t. If t is in seconds, then your sampling frequency is 100/π Hz (1Hz = 1sec-1).
By the way, MATLAB's plot connects the sampling with straight lines, there is no additional interpolation involved.