I am trying to implement the following filter on a discrete signal x:
I'm supposed to write a MATLAB function that takes a length-M (> N) vector x and a scalar N as input. The output should be a length-M vector y.
I should then test the filter with M = 50, x[n]=cos(n*pi/5)+dirac[n-30]-dirac[n-35] and N = 4, 8, 12.
Here is my try, which returns Inf with the given input and N:
function y = filt( x, N )
% filter function
if(~isvector(x))
error('Input must be a vector')
end
y = zeros(1,length(x));
temp = zeros(1,length(x));
n=1;
for v = x(:)
temp(n) = v(n);
if(n <= N-1)
y(n) = max(x);
n = n+1;
elseif(n >= N-1)
y(n) = max(temp);
end
end
end
I also tried using the built-in filter function but I can't get it to work.
Code for using the filter:
p = zeros(1,50);
for i=0:50
p(i+1)= cos(i*pi/5)+dirac(i-30)-dirac(i-35)
end
y = filt(p,4)
Thanks in advance.
That's because dirac(0) gives you Inf. This will happen in two places in your signal, where n=30 and n=35. I'm assuming you want the unit impulse instead. As such, create a signal where at n = 31 and n = 36, the output is 1, then add this with your cosine signal. This is because MATLAB starts indexing at 1 and not 0, and so dirac[0] would mean that the first point of your signal is non-zero, so translating this over by 30: dirac[n-30] would mean that the 31st point is non-zero. Similar case for dirac[n-35], so the 36th point is non-zero:
p = zeros(1,50);
p(31) = 1; p(36) = 1;
p = p + cos((0:49)*pi/5);
y = filt(p,4);
I also have some reservations with your code. It doesn't do what you think it's doing. Specifically, I'm looking at this section:
n=1;
for v = x(:)
temp(n) = v(n);
if(n <= N-1)
y(n) = max(x);
n = n+1;
elseif(n >= N-1)
y(n) = max(temp);
end
end
Doing v = x(:) would produce a column vector, and using a loop with a column vector will have unintentional results. Specifically, this loop will only execute once, with v being the entire signal. You also aren't checking the conditions properly for each window. You are doing max(x), which applies the maximum to the entire signal, and not the window.
If I can suggest a rewrite, this is what you should be doing instead:
function y = filt( x, N )
% filter function
if(~isvector(x))
error('Input must be a vector')
end
y = zeros(1,length(x));
%///// CHANGE
for n = 1 : numel(x)
if (n <= N)
y(n) = max(x(1:n));
else
y(n) = max(x(n:-1:n-N+1));
end
end
end
Take note that the if statement is n <= N. This is because in MATLAB, we start indexing at 1, but the notation in your equation starts indexing at 0. Therefore, instead of checking for n <= N-1, it must now be n <= N.
Related
so I'm new to Matlab and had to draw the Impulsefunction with y(n) is only 1 if n == 3, else 0. The following code works:
n = -5:5;
f = n; % allocate f
for i = 1 : length(n)
f(i) = dd1(n(i)-3);
end
stem(n, f);
function y = dd1(n)
y = 0;
if n == 0
y = 1;
end
end
But I feel like it's to complicated, so I tried the following:
n = -5:5
stem(n, fo)
function y = fo(n)
y = 0
if n == 3
y=1
end
end
This returns
Not enough input arguments.
Error in alternative>fo (line 5)
if n == 3
Error in alternative (line 2)
stem(n, fo)
I feel like I'm missing something trivial here.
if is no vector-wise operation but expects a single boolean (or at least a scalar that it can cast to a boolean).
But you can do this vector-wise:
lg = n == 3;
This produces a logical (MATLAB's name for boolean) array (because n is an array and not a vector), which is true where n is equal (==) to three. So you don't need a function, because you can make use of MATLAB's ability to work with vectors and arrays implicitly.
(for your code it would be f = (n-3) == 3)
A last hint: if you have a state-space system (ss-object), you can use the function step to get the step-response as a plot.
One of the methods to compute sqrt(a), a>0 is
X(n+1) = (a + (X(n)*X(n-1))/(X(n)+X(n-1)), n = 1, 2, …,
with X0=1 and X1=a (That is, it is known that lim n-> infin of Xn = sqrt(a)
Write a function [sqa, nitr] = mySqrt(a) which implements this calculation. The function should use a while-loop, terminate when the difference between Xn+1 and Xn becomes smaller than eps(10*a), and output Xn+1 in sqa and the value of n at which the while-loop was terminated in nitr. Test your function for a = 103041.
I have written this but it does not work
function [sqa, nitr] = mySqrt (a)
%[sqa, nitr] = mySqrt (a)
% computes square root of a
% sqa = a;
sqaprev = a;
nitr = 0;
X(n+1) = (a + (X(n)*X(n-1))/(X(n)+X(n-1))); %find the second term
sqa= X(n+1)
while abs (sqaprev-sqa) >= eps (10*a)
sqaprev = sqa;
sqa = (1/2) *(sqaprev+ (a/sqaprev));
nitr = nitr + 1;
end %while
end
i get the error:
Unrecognized function or variable 'X'.
Error in mySqrt (line 7)
X(n+1) = (a + (X(n)*X(n-1))/(X(n)+X(n-1))); %find the second term
Could someone help me ?
You should start with declaring your variables and assigning them values
X(1)=1;
X(2)=a;
n=2;
Then in the loop you apply the given recursion formula, not the Heron/Babylonian formula that got from somewhere else.
According to the algorithm you presented for the square root, you can try the code below
function [sqa, n] = mySqrt(a)
n = 2; % start from 2
X = [1,a]; % initial value for sequence X
while true % repeat procedure until termination condition is reached
X(n+1) = (a + (X(n)*X(n-1)))/(X(n)+X(n-1)); % update sequence X by assigning new values
if abs(X(n+1)-X(n)) <= eps(10*a) % termination condition
break;
end
n = n + 1;
end
sqa = X(end); % return the last element of X as the square root
end
such that
>> [sqa,n] = mySqrt(a)
sqa = 321.00
n = 20
I am trying to plot a discrete ramp sequence using Matlab, within the interval [-10, 10].
This is my code:
function Ramp()
rampseq(-10, 10);
end
function rampseq (n1, n2)
n = (n1:1:n2);
stem (n, pw(n));
end
function y = pw(n)
if (n < 0)
y = 0;
return;
else
y = n;
return;
end
end
I define the behavior of the sequence in the pw(n) function (short form for 'piecewise'). Note that if n < 0, the output should be 0 or else if n >= 0, the output should be n itself. However, the plot turns out to be:
This isn't the ramp sequence as the Y-values are not 0 when n < 0, contrary to the behavior defined in the pw(n) function. Where am I going wrong? Is the if statement being skipped for some reason? The Command Window does not show any error.
You are passing the whole vector n into the pw() function. However, the pw() function then compares n to 0, which is a scalar.
You could adjust your pw() function to operate on vector inputs like this:
function y = pw(n)
y = n;
y(n < 0) = 0;
end
below is my code to perform jacobi iterations to solve Ax=b.
I try this code on the matrix A =[4 -1 1; 4 -8 1; -2 1 5] and b=[7 -21 15].
and x is a first guess 1 x 3 vector. Are not these dimensions correct? It gives me the error in the code that calculates: r = b - x*A
and M\(x*N + b)
What am I missing?!? how do I fix this? please help!
function [x, error, iter, flag] = jacobi(A, x, b, maxiter, tol)
%implement jacobi iterations
%[x, error, iter, flag] = jacobi(A, x, b, maxiter, tol)
%jacobi.m solves the linear system Ax=b using the Jacobi iteration
%
%
%INPUT A the matrix of the system Ax=b
% x the first guess vector Ax=b
% b the vector in the system
% maxiter the maximum number of iteration to perform
% tol the tolerance
%
%OUTPUT x the solution vector
% error error norm
% niter the number of iterations it took
% flag indicates whether a solution was found. 0 means there was a
% solution and 1 means there was not a solution
iter = 0;
flag = 0;
bnrm2 = norm(b);
if (bnrm2 == 0)
bnrm2 = 1.0;
end
r = b - x*A;
error = norm(r) / bnrm2;
if (error<tol)
return;
end
[m,n] = size(A);
M = diag(diag(A));
N = diag(diag(A)) - A;
for iter = 1:maxiter,
oldx = x;
x = M\(x*N + b);
error = norm(x - oldx) / norm(x);
if (error <= tol)
break;
end
end
if (error > tol)
flag = 1;
end
Since, in the code, you're solving what I'll call (not sure if it's proper since I never do it) the left-multiply problem, the operator and order of matrices are, in some sense, reversed.
If you were solving the problem A*x = b with the residual r = b - A*x (i.e., x and b are column vectors), you would perform right-vector multiplies and left-matrix divides. Therefore, the update line in the loop would be
x = M \ (N*x + b);
Conversely, if you were solving the problem x*A = b with the residual r = b - x*A (i.e., x and b are row vectors), you would perform left-vector multiplies and right-matrix divides. Therefore, the update line in the loop would be
x = (x*N + b) / M;
Note that \ resolves to the function mldivide and / resolves to mrdivide. There is no function distinction for the multiply.
It appears your current updater mixes the two, which is bad news bears for dimension matching.
I can't seem to find a fix to my infinite loop. I have coded a Jacobi solver to solve a system of linear equations.
Here is my code:
function [x, i] = Jacobi(A, b, x0, TOL)
[m n] = size(A);
i = 0;
x = [0;0;0];
while (true)
i =1;
for r=1:m
sum = 0;
for c=1:n
if r~=c
sum = sum + A(r,c)*x(c);
else
x(r) = (-sum + b(r))/A(r,c);
end
x(r) = (-sum + b(r))/A(r,c);
xxx end xxx
end
if abs(norm(x) - norm(x0)) < TOL;
break
end
x0 = x;
i = i + 1;
end
When I terminate the code it ends at the line with xxx
The reason why your code isn't working is due to the logic of your if statements inside your for loops. Specifically, you need to accumulate all values for a particular row that don't belong to the diagonal of that row first. Once that's done, you then perform the division. You also need to make sure that you're dividing by the diagonal coefficient of A for that row you're concentrating on, which corresponds to the component of x you're trying to solve for. You also need to remove the i=1 statement at the beginning of your loop. You're resetting i each time.
In other words:
function [x, i] = Jacobi(A, b, x0, TOL)
[m n] = size(A);
i = 0;
x = [0;0;0];
while (true)
for r=1:m
sum = 0;
for c=1:n
if r==c %// NEW
continue;
end
sum = sum + A(r,c)*x(c); %// NEW
end
x(r) = (-sum + b(r))/A(r,r); %// CHANGE
end
if abs(norm(x) - norm(x0)) < TOL;
break
end
x0 = x;
i = i + 1;
end
Example use:
A = [6 1 1; 1 5 3; 0 2 4]
b = [1 2 3].';
[x,i] = Jacobi(A, b, [0;0;0], 1e-10)
x =
0.048780487792648
-0.085365853612062
0.792682926806031
i =
20
This means it took 20 iterations to achieve a solution with tolerance 1e-10. Compare this with MATLAB's built-in inverse:
x2 = A \ b
x2 =
0.048780487804878
-0.085365853658537
0.792682926829268
As you can see, I specified a tolerance of 1e-10, which means we are guaranteed to have 10 decimal places of accuracy. We can certainly see 10 decimal places of accuracy between what Jacobi gives us with what MATLAB gives us built-in.