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What is the computatinal complexity of resample(x,p,q)?

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Kalasagarreddi Kottakota
Kalasagarreddi Kottakota am 2 Dez. 2023
Beantwortet: Ravi am 21 Dez. 2023
Hi I am perform downsampling with resample(x,p,q) in matlab and need to find the computational complexity of it.
y = resample(x,p,q) resamples the input sequence, x, at p/q times the original sample rate. resample applies an FIR Antialiasing Lowpass Filter to x and compensates for the delay introduced by the filter. The function operates along the first array dimension with size greater than 1.
Let N be the total number of samples, for FIR lowpass filter, the computational complexity is O(N*L), with L being number of filter taps
Decimination: Let p = 1
Then for a signal of N samples what is the time complexity of decimination for p/q with p =1?

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Ravi am 21 Dez. 2023
Hi Kalasagarreddi Kottakota,
I assume that you want to know the overall complexity of the “resample” function provided “p = 1”.
The decimation process involves two main steps:
1. Filtering the signal to avoid aliasing.
2. Down-sampling the signal by selecting every q-th sample after filtering.
For the down-sampling process, when p = 1, you are simply selecting every qth sample from the filtered signal. If the original signal has N samples, after filtering, you still have N samples, but you will only keep every qth sample. Therefore, the number of samples in the down-sampled signal will be approximately N/q.
The computational complexity of the down-sampling process is proportional to the number of samples in the down-sampled signal. Since we are only selecting every qth sample, the complexity of this step is O(N/q).
Combining the two steps, we have:
1. Filtering: O(N*L)
2. Down-sampling: O(N/q)
The overall complexity is the sum of the complexities of these two steps. However, since O(N*L) is typically much larger than O(N/q) (especially for large L), the filtering step dominates the computational complexity. Therefore, the overall complexity of the decimation process when p = 1 is approximately O(N*L).
Hope this explanation solves your question.
Ravi Chandra

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