In this simple case, you could get by with using

sum(x.*x)

It seems times (.*) is supported properly for integer matrices, although mtimes ( *) is not.

For general matrix multiplication: let A and B be two matrices with suitable sizes so that A*B exists. Since times and sum are supported for integers, you can generalize the above trick, usingbsxfun and sum to compute all entries of the product matrix as follows.

Edit: As noted by @July, you need the 'native' flag in sum in order to keep the result of integer type. Thanks also for pointing out a problem that was caused by squeeze, now corrected by using a second permute.

permute(sum(bsxfun(@times, A.', permute(B, [1 3 2])), 1, 'native'), [2 3 1])

For example:

>> A = int64([1 2; 3 4])
A =
                    1                    2
                    3                    4
>> B = int64([5 7 9; 6 8 10])
B =
                    5                    7                    9
                    6                    8                   10
>> permute(sum(bsxfun(@times, A.', permute(B, [1 3 2])), 'native'), [2 3 1])
ans =
    17    23    29
    39    53    67

Anyway, the fastest alternative seems to be double(A)*double(B).

The dimensions 1x1 means a scalar. Thus you have the product between a scalar and a matrix.

You just need to cast the data to double, then run your code again. Basically what the error is saying is that you are trying to mix classes of data together when applying a matrix multiplication between two variable. Specifically, the numerical vectors and matrices you define in dft1 are all of a double type, yet your image is probably of type uint8 when you read this in through imread. This is why you're getting that integer error because uint8 is an integer class and you are trying to perform matrix multiplication with this data type with those of a double data type. Bear in mind that you can mix data types, so long as one number is a single number / scalar. This is also what the error is alluding to. Matrix multiplication of varaibles that are not floating point (double, single) is not supported in MATLAB so you need to make sure that your image data and your DFT matrices are the same type before applying your algorithm.

As such, simply do:

I = imread('sample.jpg');
R = dft1(double(I));

Minor Note

This code is quite clever, and it (by default) applies the 1D DFT to all columns of your image. The output will be a matrix of the same size as I where each column is the 1D DFT result of each column from I.

This is something to think about, but should you want to apply this to all rows of your image, you would simply transpose I before it goes into dft1 so that the rows become columns and you can operate on these new "columns". Once you're done, you simply have to transpose the result back so that you'll get your output from dft1 shaped such that the results are applied on a per row basis. Therefore:

I = imread('sample.jpg');
R = dft1(double(I.')).';

Hope this helps! Good luck!