How to convolve two equations

I am trying to convolve two functions.

f(s) = (1-4s^2)^0.5

v(s) = sinc(s/pi)-0.5(sinc(s/2*pi))^2

I followed with entering in this:

w = conv(f,v,'full');

I keep getting an error. Would anyone know how to help? I'm not sure where I am going wrong?

[M]

What is the error you get ? How do you define s ?

[John D'Errico]

There are a few potential problems here.

1. Sinc uses the Signal Processing Toolbox.

2. This is not valid MATLAB code:

v(s) = sinc(s/pi)-0.5(sinc(s/2*pi))^2

Multiplication requires an "*". Leaving it out will generate an error. So depending on whats is, you might have done this:

v = sinc(s/pi)-0.5*(sinc(s/2*pi))^2

If s is a vector, then you needed to use a dot operator, though scalar multiplication and division are ok with * and / alone.

v = sinc(s/pi)-0.5*(sinc(s/2*pi)).^2

Likewise, f has problems. Note that this relation only lives for real values on the interval [-0.5,0.5]. As well, you need to use dot operators again for vector s. And again, multiplication REQUIRES an *.

f = sqrt(1-4*s.^2);

3. Were you wanting to do a symbolic convolution?

[Asima Warner]

Hi John, I did download the Signal Processing Toolbox. I am still pretty new to MatLab and am still learning the ropes. Thank you for pointing the typing errors out. I would have never noticed. What is the difference between a symbolic convolution and a normal convolution?

[Asima Warner]

M, this is the error I am receiving.

Error using conv2 Invalid data type. First and second arguments must be numeric or logical.

Error in conv (line 43) c = conv2(a(:),b(:),shape);

Error in CT_ComputerProject_Week8 (line 60) w = conv(v(:),s(:),'full');

[Walter Roberson]

Did you create

s = tf('s')

or using

syms s

? Either way, conv() is not valid for those.

[Asima Warner]

I used syms s on a previous section of this problem. I was plotting a ram-lak filter and used this code:

 syms s v  
 f(s, v) = sinc(s./pi)-0.5*sinc(s./(2*pi))^2;
 ezplot(f, [-1,1])

Would that be affecting the conv? If so, would you have any suggestions on what to do?

Answer 1

[Walter Roberson]

conv() is for discrete convolution. The use of symbolic variables implies continuous convolution. For that, you can use the fourier equivalence, that convolution in time is equivalent to addition in frequency.

syms s t
f(s) = sqrt(1-4*s^2)
v(s) = sinc(s/pi)-0.5*(sinc(s/2*pi))^2
fv = simplify(ifourier(fourier(f,s,t)+fourier(v,s,t),t,s))

[Asima Warner]

I entered what you have provided and added

 imshow(fv)

to display fv, but am receiving this error

Error using imageDisplayValidateParams Expected input number 1, I, to be one of these types:

numeric, logical

Instead its type was sym.

Error in images.internal.imageDisplayValidateParams (line 11) validateattributes(common_args.CData, {'numeric','logical'},...

Error in images.internal.imageDisplayParseInputs (line 78) common_args = images.internal.imageDisplayValidateParams(common_args);

Error in imshow (line 241) images.internal.imageDisplayParseInputs({'Parent','Border','Reduce'},preparsed_varargin{:});

Error in CT_ComputerProject_Week8 (line 62) imshow(fv)

Am I interpreting your code incorrectly? fv is the convolution between f(s) and v(s) and should be able to be displayed via imshow.

[Taylor Artunian]

Convolution in time domain is equivalent to multiplication in frequency.