y = pulstran(___,intfunc)
specifies alternative interpolation methods. See interp1 for a
list of available methods. You can use this parameter with any of the previous input
syntaxes.

This example generates a pulse train using the default rectangular pulse of unit width. The repetition frequency is 0.5 Hz, the signal length is 60 s, and the sample rate is 1 kHz. The gain factor is a sinusoid of frequency 0.05 Hz.

t = 0:1/1e3:60;
d = [0:2:60;sin(2*pi*0.05*(0:2:60))]';
x = @rectpuls;
y = pulstran(t,d,x);
plot(t,y)
hold off
xlabel('Time (s)')
ylabel('Waveform')

This example generates an asymmetric sawtooth waveform with a repetition frequency of 3 Hz. The sawtooth has width 0.2 s and skew factor –1. The signal length is 1 s, and the sample rate is 1 kHz. Plot the pulse train.

fs = 1e3;
t = 0:1/1e3:1;
d = 0:1/3:1;
x = tripuls(t,0.2,-1);
y = pulstran(t,d,x,fs);
plot(t,y)
hold off
xlabel('Time (s)')
ylabel('Waveform')

Plot a 10 kHz Gaussian RF pulse with 50% bandwidth, sampled at a rate of 10 MHz. Truncate the pulse where the envelope falls 40 dB below the peak.

fs = 1e7;
tc = gauspuls('cutoff',10e3,0.5,[],-40);
t = -tc:1/fs:tc;
x = gauspuls(t,10e3,0.5);
plot(t,x)
xlabel('Time (s)')
ylabel('Waveform')

The pulse repetition frequency is 1 kHz, the sample rate is 50 kHz, and the pulse train length is 25 ms. The gain factor is a sinusoid of frequency 0.1 Hz.

ts = 0:1/50e3:0.025;
d = [0:1/1e3:0.025;sin(2*pi*0.1*(0:25))]';
y = pulstran(ts,d,x,fs);

Write a function that generates custom pulses consisting of a sinusoid damped by an exponential. The pulse is an odd function of time. The generating function has a second input argument that specifies a single value for the sinusoid frequency and the damping factor. Display a generated pulse, sampled at 1 kHz for 1 second, with a frequency and damping value, both equal to 30.

Use the pulstran function to generate a train of custom pulses. The train is sampled at 2 kHz for 1.2 seconds. The pulses occur every third of a second and have exponentially decreasing amplitudes.

Initially specify the generated pulse as a prototype. Include the prototype sample rate in the function call. In this case, pulstran replicates the pulses at the specified locations.

fs = 2e3;
t = 0:1/fs:1.2;
d = 0:1/3:1;
dd = [d;4.^-d]';
z = pulstran(t,dd,pp,ffs);
plot(t,z)
xlabel('Time (s)')
ylabel('Waveform')

Generate the pulse train again, but now use the generating function as an input argument. Include the frequency and damping parameter in the function call. In this case, pulstran generates the pulse so that it is centered about zero.

y = pulstran(t,dd,fnx,30);
plot(t,y)
xlabel('Time (s)')
ylabel('Waveform')

Write a function that generates a custom exponentially decaying sawtooth waveform of frequency 0.25 Hz. The generating function has a second input argument that specifies a single value for the sawtooth frequency and the damping factor. Display a generated pulse, sampled at 0.1 kHz for 1 second, with a frequency and damping value equal to 50.

Use the pulstran function to generate a train of custom pulses. The train is sampled at 0.1 kHz for 125 seconds. The pulses occur every 25 seconds and have exponentially decreasing amplitudes.

Specify the generated pulse as a prototype. Generate three pulse trains using the default linear interpolation method, nearest neighbor interpolation and piecewise cubic interpolation. Compare the pulse trains on a single plot.

d = [0:25:125; exp(-0.015*(0:25:125))]';
ffs = 100;
tp = 0:1/ffs:125;
r = pulstran(tp,d,pp);
y = pulstran(tp,d,pp,'nearest');
q = pulstran(tp,d,pp,'pchip');
plot(tp,r)
hold on
plot(tp,y)
plot(tp,q)
xlim([0 125])
legend('Linear interpolation','Nearest neighbor interpolation','Piecewise cubic interpolation')
hold off

Time values at which func is evaluated, specified as a
vector.

d — Offset row vector | two-column matrix

Offset removed from the values of the array t, specified as a
real vector. You can apply an optional gain factor to each delayed evaluation by
specifying d as a two-column matrix, with offset defined in column
1 and associated gain in column 2. If you specify d as a row
vector, the values are interpreted as delays only.

func — Continuous function 'rectpuls' | 'gauspuls' | 'tripuls' | function handle

Continuous function used to generate a pulse train based on its samples, specified
as 'rectpuls', 'gauspuls',
'tripuls', or a function handle.

If you use func as a function handle, you can pass the function
parameters as follows:

y = pulstran(t,d,'gauspuls',10e3,0.5);

This creates a pulse train using a 10 kHz Gaussian pulse with 50% bandwidth.

p — Prototype pulse vector

Prototype function, specified as a vector. The interval of p is
given by [0,(length(p)-1)/fs], and its samples are identically zero
outside this interval. By default, linear interpolation is used for generating
delays.

Interpolation method, specified as one of the options in this
table.

Method

Description

Continuity

Comments

'linear'

Linear interpolation. The interpolated value at a query point is
based on linear interpolation of the values at neighboring grid points in
each respective dimension. This is the default interpolation
method.

C^{0}

Requires at least 2 points

Requires more memory and computation time than nearest
neighbor

'nearest'

Nearest neighbor interpolation. The interpolated value at a query
point is the value at the nearest sample grid point.

Discontinuous

Requires at least 2 points

Modest memory requirements

Fastest computation time

'next'

Next neighbor interpolation. The interpolated value at a query
point is the value at the next sample grid point.

Discontinuous

Requires at least 2 points

Similar memory requirements and computation time as
'nearest'

'previous'

Previous neighbor interpolation. The interpolated value at a query
point is the value at the previous sample grid point.

Discontinuous

Requires at least 2 points

Similar memory requirements and computation time as
'nearest'

'pchip' or
'cubic'

Shape-preserving piecewise cubic interpolation. The interpolated
value at a query point is based on a shape-preserving piecewise cubic
interpolation of the values at neighboring grid points.

C^{1}

Requires at least 4 points

Requires more memory and computation time than
'linear'

'v5cubic'

Cubic convolution used in MATLAB^{®} 5.

C^{1}

Points must be uniformly spaced.

'makima'

Modified Akima cubic Hermite interpolation. The interpolated value
at a query point is based on a piecewise function of polynomials with a
degree of at most three. The Akima formula is modified to avoid
overshoots.

C^{1}

Requires at least 2 points

Produces fewer undulations than 'spline', but
does not flatten as aggressively as 'pchip'

Computation is more expensive than 'pchip', but
typically less than 'spline'

Memory requirements are similar to those of
'spline'

'spline'

Spline interpolation using not-a-knot end conditions. The
interpolated value at a query point is based on a cubic interpolation of the
values at neighboring grid points in each respective
dimension.

C^{2}

Requires at least 4 points

Requires more memory and computation time than
'pchip'

You can also select a web site from the following list:

How to Get Best Site Performance

Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.