idinput

Generate a single-channel random binary input signal with 200 samples.

N = 200;
u = idinput(N);

u is a column vector of length 200. The values in u are either -1 or 1.

Create an iddata object from the generated signal. For this example, specify the sample time as 1 second.

u = iddata([],u,1);

To examine the signal, plot it.

plot(u)

The generated signal is a random binary input signal with values -1 or 1. You can use the generated input signal to simulate the output of your system using the sim command.

Generate a two-channel random binary input signal with 200 samples.

N = 200;
u = idinput([N,2]);

u is a 200-by-2 matrix with values -1 or 1.

Create an iddata object from the generated signal. For this example, specify the sample time as 1 second.

u = iddata([],u,1);

Plot the signals for the two channels, and examine the signals.

plot(u)

The plot shows the two generated random binary signals with values -1 or 1.

Generate a single-channel periodic random binary input signal with a period of 10 samples and 5 periods in the signal.

NumChannel = 1;
Period = 10;
NumPeriod = 5;
u = idinput([Period,NumChannel,NumPeriod]);

u is a column vector of length 50 (= Period*NumPeriod). The values in u are either -1 or 1.

Create an iddata object from the generated signal. Specify the sample time as 1 second.

u = iddata([],u,1);

Plot the signal.

plot(u)

As specified, the generated single-channel periodic random binary input signal has a period of 10 seconds, and there are 5 whole periods in the signal.

Generate a single-channel periodic random Gaussian input signal with a period of 50 samples and 5 periods in the signal. First generate the signal using the entire frequency range, then specify a passband.

NumChannel = 1;
Period = 50;
NumPeriod = 5;
u = idinput([Period,NumChannel,NumPeriod],'rgs');

u is a column vector of length 250 (= Period*NumPeriod).

Create an iddata object from the generated signal, and plot the signal. For this example, specify the sample time as 0.01 seconds.

u = iddata([],u,0.01);
plot(u)

The plot shows that u contains a random segment of 50 samples, repeated 5 times. The signal is a Gaussian white noise signal with zero mean and variance one.

Since the sample time is 0.01 seconds, the generated signal has a period of 0.5 seconds. The frequency content of the signal spans the entire available range (0-50 Hz).

Now specify a passband between 0 and 25 Hz ( = 0.5 times the Nyquist frequency).

Band = [0 0.5];
u2 = idinput([Period,NumChannel,NumPeriod],'rgs',Band);

Create an iddata object, and plot the signal.

u2 = iddata([],u2,0.01);
plot(u2)

The frequency content of the generated signal u2 is limited to 0-25 Hz.

A pseudorandom binary input signal (PRBS) is a deterministic signal whose frequency properties mimic white noise. A PRBS is inherently periodic with a maximum period length of $$2^n-1$$, where integer n is the order of the PRBS. For more information, see Pseudorandom Binary Signals.

Specify that the single-channel PRBS value switches between -2 and 2.

Range = [-2,2];

Specify the clock period of the signal as 1 sample. That is, the signal value can change at each time step. For PRBS signals, the clock period is specified in Band = [0 B], where B is the inverse of the required clock period.

Band = [0 1];

Generate a nonperiodic PRBS of length 100 samples.

u = idinput(100,'prbs',Band,Range);

Warning: The PRBS signal delivered is the 100 first values of a full sequence of length 127.

A PRBS is inherently periodic. To generate a nonperiodic signal, the software generates a maximum length PRBS of length 127 that has a period greater than the required number of samples, 100. The software returns the first 100 samples of the generated PRBS. This action ensures that the generated signal is not periodic, as indicated in the generated warning.

Create an iddata object from the generated signal. For this example, specify the sample time as 1 second.

u = iddata([],u,1);

Plot, and examine the generated signal.

plot(u);
title('Non-Periodic Signal')

The generated signal is a nonperiodic PRBS of length 100 that switches between -2 and 2.

Specify that the pseudorandom binary input signal (PRBS) switches between -2 and 2.

Range = [-2,2];

Specify the clock period of the signal as 1 sample. That is, the signal value can change at each time step. For PRBS signals, the clock period is specified in Band = [0 B], where B is the inverse of the required clock period.

Band = [0 1];

Generate a single-channel, periodic PRBS with a period of 100 samples and 3 periods in the signal.

u1 = idinput([100,1,3],'prbs',Band,Range);

Warning: The period of the PRBS signal was changed to 63. Accordingly, the length of the generated signal will be 189.

A PRBS is inherently periodic with a maximum period length of $$2^n-1$$, where integer n is the order of the PRBS. If the period you specify is not equal to a maximum length PRBS, the software adjusts the period of the generated signal to obtain an integer number of maximum length PRBS, and issues a warning. For more information about maximum length PRBS, see Pseudorandom Binary Signals. In this example, the desired period, 100, is not equal to a maximum length PRBS, thus the software instead generates a maximum length PRBS of order n = floor(log2(Period)) = 6. Thus, the period of the PRBS signal is 63 ( = $$2^6-1$$), and the length of the generated signal is 189 (= NumPeriod*63). This result is indicated in the generated warning.

Create an iddata object from the generated signal, and plot the signal. Specify the period of the signal as 63 samples.

u1 = iddata([],u1,1,'Period',63);
plot(u1)
title('Periodic Signal')

The generated signal is a periodic PRBS with three periods.

Generate periodic and nonperiodic pseudorandom binary input signals (PRBS) with specified clock period.

Generate a single-channel PRBS that switches between -2 and 2. Specify the clock period of the signal as 4 samples. That is, the signal has to stay constant for at least 4 consecutive samples before it can change. For PRBS signals, the clock period is specified in Band = [0 B], where B is the inverse of the required clock period.

Range = [-2,2];
Band = [0 1/4];

First generate a nonperiodic signal of length 100.

u1 = idinput(100,'prbs',Band,Range);

Warning: The PRBS signal delivered is the 100 first values of a full sequence of length 124.

To understand the generated warning, first note that the code is equivalent to generating a single-channel PRBS with a 100-sample period and 1 period.

u1 = idinput([100,1,1],'prbs',Band,Range);

The generated PRBS signal has to remain constant for at least 4 samples before the value can change. To satisfy this requirement, the software first computes the order of the smallest possible maximum length PRBS as n = floor(log2(Period*B)) = 4 and period $$2^n-1=15$$. For information about maximum length PRBS, see Pseudorandom Binary Signals. The software then stretches this PRBS such that the period of the stretched signal is $$P=(1/B)(2^n-1)=60$$.

However, since this period is less than the specified length, 100, the software computes instead a maximum length PRBS of order m = n+1 = 5. The software then stretches this PRBS such that the period is now $$P2=(1/B)(2^m-1)=124$$. The software returns the first 100 samples of this signal as u1. This result ensures that the generated signal is not periodic but is constant for every 4 samples.

Create an iddata object from the generated signal. For this example, specify the sample time as 1 second.

u1 = iddata([],u1,1);

Plot, and examine the signal.

plot(u1);
title('Nonperiodic Signal')

The generated signal is a nonperiodic PRBS of length 100. The signal remains constant for at least 4 samples before each change in value. Thus, the signal satisfies the clock period specified in Band.

Now generate a periodic signal with a 100-sample period and 3 periods.

u2 = idinput([100,1,3],'prbs',Band,Range);

Warning: The period of the PRBS signal was changed to 60. Accordingly, the length of the generated signal will be 180.

To generate a periodic signal with specified clock period, the software generates u2 as 3 repetitions of the original stretched signal of period P = 60. Thus, the length of u2 is P*NumPeriod = 60*3 = 180. This change in period and length of the generated signal is indicated in the generated warning.

Create an iddata object from the generated signal, and plot the signal. Specify the period of the signal as 60 seconds.

u2 = iddata([],u2,1,'Period',60);
plot(u2)
title('Periodic Signal')

The generated signal is a periodic PRBS with a 60-second period and 3 periods. The signal remains constant for at least 4 samples before each change in value. Thus, the signal satisfies the specified clock period.

You can generate a sum-of-sinusoids signal using default characteristics for the sine waves. Alternatively, you configure the number of sine waves, and the frequencies and phases of the sine waves. This example shows both approaches.

Specify that the signal has 50 samples in each period and 3 periods. Also specify that the signal amplitude range is between -1 and 1.

Period = 50;
NumPeriod = 3;
Range = [-1 1];

Specify the frequency range of the signal. For a sum-of-sinusoids signal, you specify the lower and upper frequencies of the passband in fractions of the Nyquist frequency. In this example, use the entire frequency range between 0 and Nyquist frequency.

Band = [0 1];

First generate the signal using default characteristics for the sine waves. By default, the software uses 10 sine waves to generate the signal. The software assigns a random phase to each sinusoid, and then changes these phases 10 times to get the smallest signal spread. The signal spread is the difference between the minimum and the maximum value of the signal over all samples.

[u,freq] = idinput([Period 1 NumPeriod],'sine',Band,Range);

The software returns the sum-of-sinusoids signal in u and the frequencies of the sinusoids in freq. The values in freq are scaled assuming that the sample time is 1 time unit. Suppose that the sample time is 0.01 hours. To retrieve the actual frequencies in rad/hours, divide the values by the sample time.

Ts = 0.01; % Sample time in hours
freq = freq/Ts;
freq(1)

ans = 
12.5664

freq(1) is the frequency of the first sine wave. To see how the software chooses the frequencies, see the SineData argument description on the idinput reference page.

To verify that 10 sine waves were used to generate the signal, you can view the frequency content of the signal. Perform a Fourier transform of the signal, and plot the single-sided amplitude spectrum of the signal.

ufft = fft(u);
Fs = 2*pi/Ts; % Sampling frequency in rad/hour
L = length(u);
w = (0:L-1)*Fs/L;
stem(w(1:L/2),abs(ufft(1:L/2))) % Plot until Nyquist frequency
title('Single-Sided Amplitude Spectrum of u(t)')
xlabel('Frequency (rad/hour)')
ylabel('Amplitude')

The generated plot shows the frequencies of the 10 sine waves used to generate the signal. For example, the plot shows that the first sine wave has a frequency of 12.57 rad/hour, the same as freq(1).

Convert the generated signal into an iddata object, and plot the signal. Specify the sample time as 0.01 hours.

u = iddata([],u,Ts,'TimeUnit','hours');
plot(u)

The signal u is generated using 10 sinusoids and has a period of 0.5 hours and 3 periods.

Now modify the number, frequency, and phase of the sinusoids that are used to generate the sum-of-sinusoids signal. Use 12 sinusoids and try 15 different sets of phases. To set the frequencies of the sinusoids, specify GridSkip = 2. The software selects the frequencies of the sinusoids from the intersection of the frequency grid 2*pi*[1:GridSkip:fix(Period/2)]/Period and the passband pi*Band.

NumSinusoids = 12;
NumTrials = 15;
GridSkip = 2;
SineData = [NumSinusoids,NumTrials,GridSkip];
u2 = idinput([Period 1 NumPeriod],'sine',Band,Range,SineData);

Convert the generated signal into an iddata object, and plot the signal.

u2 = iddata([],u2,Ts,'TimeUnit','hours');
plot(u2)

The signal u2 is generated using 12 sinusoids and has a period of 0.5 hours and 3 periods.