Time invariance in matlab - matlab

How can I write a MATLAB program that takes the given system described in terms input x(t) and output
y(t) relations is input and finds out whether it is time-invariant or not?

From here:
If the input signal x(t) produces an output y(t) then any time shifted
input, x(t + \delta), results in a time-shifted output y(t + \delta)
So all you have to do is input a signal and store its output. Then delay (i.e., shift) the input signal by some amount and then see if the output is a shifted version of the earlier one (with the shift being equal to the amount by which the input signal was shifted). With the information provided, it's impossible to say if there are certain classes of signals for which the above test would fail. However, if this is for homework or something, any old signal would probably do.

Related

correct sampling points for FFT

I want to calculate the Fourier series of a signal using FFT on matlab. And I came across the following unexpected issue. Mere example
If I define a grid and then compute the fft as:
M=59;
x= deal(1*(0:M-1)/M);
y=3*cos(2*pi*x);
Yk=fftshift(fft2(y)/(M));
which gives me the exact analytic values expected: Yk(29)=1.5; Yk(31)=1.5; zeros anything else
but if I define the grid as, and repeat the fft calculation:
x=0:1/(M-1):1;
y=3*cos(2*pi*x);
Yk=fftshift(fft2(y)/(M));
got the Yk's values completely screwed up
This is an annoying issue since I have to analyse many signals data that was sampled as in the second method so the Yk's values will be wrong. Is there a way to workaround this? an option to tell something to the fft function about the way the signal was sampled. Have no way to resample the data in the correct way.
The main reason to avoid have spectral leaking, is that I do further operations with these Fourier terms individually Real and Imag parts. And the spectral leaking is messing the final results.
The second form of sampling includes one sample too many in the period of the cosine. This causes some spectral leaking, and adds a small shift to your signal (which leads to non-zero imaginary values). If you drop the last point, you'll cosine will again be sampled correctly, and you'll get rid of both of these effects. Your FFT will have one value less, I don't know if this will affect your analyses in any way.
x = 0:1/(M-1):1;
y = 3*cos(2*pi*x);
Yk = fftshift(fft2(y(1:end-1))/(M-1));
>> max(abs(imag(Yk)))
ans =
1.837610523517500e-16

Matlab inverse fast fourier tansform for frequency-wavenumber field, do I need make conjugation and flip?

First I describe the physics, it is in a axisymmetric space, one sound source was placed at the original point, one sensor was placed on the axis under the source. Giving the source wave form, I try to get the sensor's waveform. all materiel parameter were known, for instance, sound speed, density.
I write the Matlab script to calculate it, by solving the sound propagation equation I can get
one function, say, A(w,k), w is frequency and k is wavenumber, this is so called frequency-wavenumber field. My matlab code like this,
discrete w and k, get a A array. first use FFT to k, get space and frequency information
then, FFT to w, get space and time information, that is the waveform at different point.
the fake code
for i_w=...
w=...
for i_k=...
k=...
M=A(w,k)
end
wave_space_freq=ifft(M)
end % here can specify the only point of the sensor
wave_space_freq=ifft(wave_space_freq)
My question is do I need to make conjugation and flip when I use IFFT,like ifft(M,0,fliplr(conj(M))) . because I saw some-others use them, but I don't understand why?
If you want a strictly real-valued result waveform (not complex with significant imaginary components), then the input to an IFFT has to be conjugate symmetric, such as:
ifft(dc_term,M,0,fliplr(conj(M))).

DTMF, DFT window length

We've got an assignment in school to create a DTMF decoder, but are having trouble understanding what needs to be done, and how. First of all we need to calculate the energy of the signal using convolution. We do it by making use of the window length and the absolute value of the input signal:
SmoothEnergyOfInputSignal = conv(abs(X), ones(1,winlen)/winlen); %moving average
Now, we don't know how to get the proper window length. The smoothed energy is used to segment the signal, and later to determine the different frequencies in the signal making use of basis vectors(?)
The dtmf-pulses are at least 40ms separated by at least 40ms of silence.
The sampling frequency is at 8kHz and our signal is about 17601 samples long.
We thought that by doing fs*0.04 we'd get the window length. 0.04=40ms, but now the smoothed energy signal is shifted so the segments go beyond the maximum samples of the input signal.
[Sound, fs] = audioread('dtmf_all.wav');
winlen = fs*0.04
E = conv(abs(Sound),ones(1, winlen)/winlen)
Long story short: How do we calculate the "correct" window length?
Thanks in advance.
EDIT: The instructions were updated, and we're not supposed to use convolution. We're supposed to use filter()

Continuos Signal to MATLAB Function in Simulink

How can I introduce a continuos signal to a MATLAB Function block so I can get a continuos output.
My MATLAB Function block will be this:
function y = fcn(u)
y = 2*exp(-u);
So I can get a negative exponential, this because I need a control voltage source with a negative exponential signal. I need to introduce a controlled voltage source a exponential signal, is there other way?
Thanks
First of all, you don't need a MATLAB function to do that: take your input signal, multiply it by -1 with a Gain block, then use a Math Function block set to exp, and finally another Gain block to multiply it by 2.
Second, your input signal can be whatever you want. For example, you can use a Sine Wave block, or choose whatever block you want from the Sources library. If you leave the Sample Time parameter to 0, you will have a "continuous" signal (in the Simulink sense of the word), see Specify Sample Time in the documentation for more details. You can also use your own data from the MATLAB workspace using a From Workspace block.

How to get max from Scope (Simulink)

I would like to get only one number (maximum) from sinusoid in Matlab Simulink scope. I have a voltage measurement to measure AC voltage and current measurement. I need to find max. In my example the voltage is 231V and current is 0.26. the result number is 231*0.26 = .. to multiple it I need to get the max number from sinusoid.
Thanks a lot.
Based on your description, I think that the MinMax Running Resettable block would be more appropriate for your application.
The MinMax block will take multiple scalar value inputs (or a vector input) and output the minimum or maximum value (depending on your settings) of those inputs at the current instant in time. This would be better used to compare two signals, not to find the maximum value of a particular "stream" of signal data.
So, for example, let's say that you have a Sine Wave block that is feeding into a MinMax block (which has been set to output the max value). The MinMax block will look at all of its inputs at the current instant in time and output the maximum value. However, in this case, MinMax only has one input -- the sine wave. So the output of MinMax will actually be the same as the output of the Sine Wave block.
On the other hand, MinMax Running Resettable outputs the minimum or maximum of all past inputs. So for example, if you had a sine wave with a peak value of 231 that was being fed into the u input of a MinMax Running Resettable block, then by the end of the simulation, this block will output 231. This is, of course, provided that your simulation has run long enough that the sine wave has reached its peak value.
Note that the MinMax Running Resettable block was an R input that can be used to reset the block. If you simply want to find the max value of your signal over time and do not need to reset the block, then you can go ahead and just leave this input disconnected.
i once studied matlab at engineering school and i think you need to link the output of your sinusoid to a box called minmax
http://www.mathworks.com/help/simulink/slref/minmax.html