Why is R's hamming function different from Matlab's?

Question

Why does the hamming function in R give different values to the function of the same name in Matlab?

Matlab:

hamming(76)

    0.0800
    0.0816
    0.0864
    0.0945
    0.1056
    0.1198

R:

library(gsignal)
hamming (76)

0.08695652 0.08851577 0.09318288 0.10092597 0.11169213 0.1254078

Overprint

What package is hamming from? It is not a base function. What function are you using in Matlab? Editing your question to explain in more detail what exactly you are doing may get you better, faster help - good luck! – Guck

in matlab hamming is to design hamming windows for filters. What do you mean hamming in R? – Syndactyl

Answer 1

Algorithms

They are following different formulas (same format but different coefficients) to compute Hamming windows

• In R, it is

(25/46) - (21/46) * cos(2 * pi * (0:n)/N)

which can be viewed when typing hamming

> hamming
function (n, method = c("symmetric", "periodic")) 
{
    if (!isPosscal(n) || !isWhole(n) || n <= 0)
        stop("n must be an integer strictly positive")
    method <- match.arg(method)
    if (method == "periodic") {
        N <- n
    }
    else if (method == "symmetric") {
        N <- n - 1
    }
    else {
        stop("method must be either 'periodic' or 'symmetric'")
    }
    if (n == 1) {
        w <- 1
    }
    else {
        n <- n - 1
        w <- (25/46) - (21/46) * cos(2 * pi * (0:n)/N)
    }
    w
}

• In MATLAB, the algorithm is (see https://se.mathworks.com/help/signal/ref/hamming.html)

and there are some precision difference for two coefficients

> 25/46
[1] 0.5434783
> 21/46
[1] 0.4565217

Analysis

Two reasons that make the differences

1. in gsignals::hamming, if you choose symmetric by default, you will have N <- n-1 and n <- n-1, that means the equivalent to Matlab's hamming should be hamming(76+1)
2. the approximations 0.54 and 0.46 in Matlab contribute to the deviation from R's version.

Tests with Handmade Implementations

We can implement hamming functions according to formulas from MATLAB and R, respectively, e.g.,

hamMatalb <- function(n) 0.54 - 0.46 * cos(2 * pi * (0:n) / n)
hamR <- function(n) 25 / 46 - 21 / 46 * cos(2 * pi * (0:n) / n)

and then run

> hamMatalb(75) # the same as obtained by hamming(76) in MATLAB
 [1] 0.08000000 0.08161328 0.08644182 0.09445175 0.10558687 0.11976909
 [7] 0.13689893 0.15685623 0.17950101 0.20467443 0.23219992 0.26188441
[13] 0.29351967 0.32688382 0.36174283 0.39785218 0.43495860 0.47280181
[19] 0.51111636 0.54963351 0.58808309 0.62619540 0.66370312 0.70034314
[25] 0.73585847 0.77000000 0.80252824 0.83321504 0.86184514 0.88821773
[31] 0.91214782 0.93346756 0.95202741 0.96769718 0.98036697 0.98994790
[37] 0.99637276 0.99959650 0.99959650 0.99637276 0.98994790 0.98036697
[43] 0.96769718 0.95202741 0.93346756 0.91214782 0.88821773 0.86184514
[49] 0.83321504 0.80252824 0.77000000 0.73585847 0.70034314 0.66370312
[55] 0.62619540 0.58808309 0.54963351 0.51111636 0.47280181 0.43495860
[61] 0.39785218 0.36174283 0.32688382 0.29351967 0.26188441 0.23219992
[67] 0.20467443 0.17950101 0.15685623 0.13689893 0.11976909 0.10558687
[73] 0.09445175 0.08644182 0.08161328 0.08000000

> hamR(75) # the same as obtained by gsignal::hamming(76) in R
 [1] 0.08695652 0.08855761 0.09334964 0.10129899 0.11234992 0.12642490
 [7] 0.14342521 0.16323161 0.18570516 0.21068824 0.23800559 0.26746562
[13] 0.29886168 0.33197355 0.36656897 0.40240529 0.43923112 0.47678818
[19] 0.51481302 0.55303893 0.59119778 0.62902190 0.66624601 0.70260898
[25] 0.73785576 0.77173913 0.80402141 0.83447617 0.86288979 0.88906296
[31] 0.91281211 0.93397064 0.95239015 0.96794144 0.98051542 0.99002390
[37] 0.99640019 0.99959955 0.99959955 0.99640019 0.99002390 0.98051542
[43] 0.96794144 0.95239015 0.93397064 0.91281211 0.88906296 0.86288979
[49] 0.83447617 0.80402141 0.77173913 0.73785576 0.70260898 0.66624601
[55] 0.62902190 0.59119778 0.55303893 0.51481302 0.47678818 0.43923112
[61] 0.40240529 0.36656897 0.33197355 0.29886168 0.26746562 0.23800559
[67] 0.21068824 0.18570516 0.16323161 0.14342521 0.12642490 0.11234992
[73] 0.10129899 0.09334964 0.08855761 0.08695652

and we can check the lengths of resulting windows

> length(hamMatalb(75))
[1] 76

> length(hamR(75))
[1] 76

Spectral Performance

Given n <- 75, we can take a look at the difference in the frequency domain, using freqz. We can see that the difference mainly lies in the stopband but still quite minor, which doesn't affect the filtering performance too much.

• freqz(hamR(n))

• freqz(hamMatlab(n))

Syndactyl

+1, you beat me to this portion of the answer using the exact same links and nearly identical image of the algorithm. (I still think the core problem is that gsignal::hamming(76) produces different numbers than the OP posted. Perhaps if you extended your example to manually calculate for n=76 and n=77, it would provide a little more insight.) – Chromatography

More reference for context: en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows says "Setting a0 to approximately 0.54, or more precisely 25/46, produces the Hamming window, proposed by Richard W. Hamming." This suggests Matlab is okay with approximating? (I'll duck whatever food fight that blasphemy incites ;-) – Chromatography

@Chromatography yes, from the source code of gsignal::hamming, hamming(77) in R should be identical to hamming(76) in Matlab, but then the difference comes from the approximation. – Syndactyl

Ahhh, so R does N <- n-1 but Matlab does not? That's interesting ... yes, that makes sense too. Nice, thank you for correcting me! – Chromatography

thanks, so what shall i do to have the same output of Matlab? – Overprint

@Overprint if you want to have the same output as in MATLAB, you can write your custom function, like hamMatlab in my updated answer. hamming window formula is simple, so, easy to write your own version if you don't rely on R's solution. – Syndactyl

This is a really excellent answer. Do you have a view (or reference) about whether the differences between the R and MATLAB results are meaningful (in any domain)? Obviously we don't know the application in this case, but I've never used a Hamming window so have no idea if this something it's worth remembering in case one day it comes back to bite me... – Argument

@Argument from the perspective of spectral analysis, it difference is negligible. You can see my latest update with spectral analysis. – Syndactyl

@Chromatography AFAIK, Hamming himself suggested the rounded numbers, I guess that is why MATLAB uses them. 25/46 is where the first side-lobe gets cancelled, the exact solution to Hamming’s constraint. Using 0.53836 instead one gets the lowest side-lobes, which is actually better. The rounded value sits in between these two solutions. But the difference between them is minor, and not noticeable if you are using 8 bits for your signal. – Tune