Animated Discrete Stem Plot

So I want to create an animated plot of a discrete-time complex exponential function. The simplest non-animated plot would be given by this:

n=-5:40;
x=(exp((3*4j)*n)).*(n>=0);
y=real(x);
subplot(2,1,1);
stem (n,y)
z=imag(x);
subplot(2,1,2);
stem (n,z)

How do I animate it to show the function for the different numbers of samples considered in a given interval (assuming I have a time interval specified by start second and end second and a vector containing the number of sample values in the given interval)?

I tried along these lines:

figure,hold on
xlim([min(x(:)) max(x(:))])
ylim([min(y(:)) max(y(:))])

%// Plot point by point
for k = 1:numel(x)
    stem (k,y) %// Choose your own marker here
    pause(0.001);     
end

That doesn't compile. How to achieve this? Thanks.

Answer 1

[Samayochita]

Hi Amritpal,

You're on the right track with animating a discrete-time complex exponential function, but there are a few issues with your approach: “stem(k, y)” is incorrect because k is just an index, but y is an entire vector. You need to plot only up to k at each step. Your “xlim” and “ylim” need to be set correctly for the entire range of the signal and pause(0.001) might be too fast to notice the animation.

To properly animate the function over a specified time interval with a given number of samples, we introduce the following parameters:

1. t_start and t_end → Define the time interval.
2. num_samples_vector → A vector containing different numbers of samples for different intervals.
3. Sampling step (Ts) → Determined by the number of samples in a given interval.

The modified code is as follows:

% Define time interval and number of samples 
start_time = 0; % Start second 
end_time = 2; % End second 
num_samples_vector = [10, 20, 30, 50]; % Different numbers of samples 
% Loop over different sample sizes 
for num_samples = num_samples_vector 
    % Define discrete time indices based on num_samples 
    n = linspace(-5, 40, num_samples); % Adjust sample points 
    % Compute the discrete-time complex exponential 
    x = (exp((3*4j)*n)) .* (n >= 0); 
    y = real(x); 
    z = imag(x); 
    % Create figure 
    figure; 
    % Real Part Plot 
    subplot(2,1,1); 
    hold on; 
    xlim([min(n) max(n)]); 
    ylim([min(y) max(y)]); 
    title(['Real Part of x[n] with ', num2str(num_samples), ' samples']); 
    xlabel('n'); 
    ylabel('Amplitude'); 
    grid on; 
    real_stem = stem(n(1), y(1), 'b', 'filled'); % Initial stem plot 
    % Imaginary Part Plot 
    subplot(2,1,2); 
    hold on; 
    xlim([min(n) max(n)]); 
    ylim([min(z) max(z)]); 
    title(['Imaginary Part of x[n] with ', num2str(num_samples), ' samples']); 
    xlabel('n'); 
    ylabel('Amplitude'); 
    grid on; 
    imag_stem = stem(n(1), z(1), 'r', 'filled'); % Initial stem plot 
    % Compute animation duration based on the time interval 
    total_time = end_time - start_time; 
    frame_delay = total_time / num_samples; % Time per sample 
    % Animation loop 
    for k = 1:length(n) 
        % Update real part plot 
        set(real_stem, 'XData', n(1:k), 'YData', y(1:k)); 
        % Update imaginary part plot 
        set(imag_stem, 'XData', n(1:k), 'YData', z(1:k)); 
        pause(frame_delay); % Control animation speed 
    end 
end

Hope this helps!