SciPy - next_fast_len() Function

SciPy uses the next_fast_len() method to find the next ideal size for FFT (Fast Fourier Transform) operations to make the processing efficient, improving computation speed and efficiency for large datasets. It determines the least size that is greater than or equal to the target, usually a multiple of 3 or 5 or a power of 2.

This technique reduces computing time for huge datasets and enhances performance by matching input data with the most effective FFT grid. When combined with other FFT techniques, such as fft, ifft, or large scale transformations it guarantees quicker and more precise results in signal processing and numerical applications.

Selecting therightinput sizefor FFThelpsdecreasecomputationtimeand speed up data analysis in real-worldapplicationslike signal processing or massive dataset analysis.

Syntax

Following is the syntax of the SciPy next_fast_len() method −

.next_fast_len(target, real=False)

Parameters

This method accepts the following parameters −

• target (int): The target size, for which you want to find the "next fast length." Must be positive integer.

• real (bool, optional): If True, it finds the next fast length for real-valued inputs. If False, it looks for the next fast length for complex-valued inputs.By default it is set to False.

Return Value

next_length(int): The smallest fast length greater than or equal to the target, optimized for FFT computations.

Example 1

This example demonstrates how SciPy's next_fast_len() method finds the most effective computation size to maximize FFT speed.

import numpy as np
from scipy.fft import fft, next_fast_len

prime_len = 92753  
data = np.random.standard_normal(prime_len)

# Optimize length using next_fast_len
optimal_len = next_fast_len(prime_len)

# Perform FFT with optimized length
b = fft(data, optimal_len)
print(f"Optimized FFT length: {optimal_len}")

Following is an output of the above code −

Optimized FFT length: 92928

Example 2

Consider that we are analyzing sound data set for a musical application. A prime number, 92753 samples, might be the size of the raw data. It could take longer to calculate the FFT on this prime length.

To find the next efficient size, which is more appropriate for the FFT algorithm, we use next_fast_len() method. This can reduce the computing time, enabling the application to analyze data much more fast. In the below example you can check the differnce of processing time with the original length and optimized length.

import numpy as np
from scipy.fft import fft, next_fast_len
import time

input_len = 92753  
a = np.random.standard_normal(input_len)
fast_len = next_fast_len(input_len)

# Measure processing time for original length
start_time = time.time()
original_length = fft(a) 
end_time = time.time()
time_original = end_time - start_time

# Measure processing time for optimized length
start_time = time.time()
optimized_length = fft(a, fast_len)  # FFT with next fast length (92928)
end_time = time.time()
time_fast = end_time - start_time

print(f"Original length: {input_len}")
print(f"Next fast length: {fast_len}")
print(f"Processing time with original length: {time_original:.6f} seconds")
print(f"Processing time with optimized length: {time_fast:.6f} seconds")

Following is the output of the baove code −

Original length: 92753
Next fast length: 92928
Processing time with original length: 0.019518 seconds
Processing time with optimized length: 0.002534 seconds