How to convolve two equations

2017 10 31
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更新时间：2019 12 13
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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?

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M
M 2017-10-31
What is the error you get ? How do you define s ?
John D'Errico
John D'Errico 2017-10-31
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
Asima Warner 2017-10-31
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
Asima Warner 2017-10-31
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
Walter Roberson 2017-10-31
Did you create
s = tf('s')
or using
syms s
? Either way, conv() is not valid for those.
Asima Warner
Asima Warner 2017-10-31
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?

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Walter Roberson
Walter Roberson 2017-10-31

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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))

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Asima Warner
Asima Warner 2017-10-31
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
Taylor Artunian 2019-12-13
Convolution in time domain is equivalent to multiplication in frequency.

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