File:Sinc.wav

English: A three-second fragment of the sinc function as audio (three seconds at 44100 Hz; Blackman window applied; frequency 2000 Hz).

Generated by the following Python code.

import math
import wave
import struct

# The sinc function.
def sinc(x):
    return math.sin(x) / x if not x == 0.0 else 1.0

# The Blackman window.
def blackman(length, i):
    t = i / (length - 1)
    return 0.42 - 0.5 * math.cos(t * math.pi * 2.0) + 0.08 * math.cos(t * math.pi * 4.0)

# Windowed-sinc function.
def windowed_sinc(length, frequency):
    output = []
    for i in range(length):
        sinc_phase = i - (length - 1) / 2
        output.append(sinc(sinc_phase * frequency * math.pi * 2.0) * blackman(length, i))

    return output


SAMPLE_RATE = 44100
DURATION = 3
FREQUENCY = 2000.0
with wave.open("sinc.wav", "w") as wavfile:
    wavfile.setnchannels(2)
    wavfile.setsampwidth(2)
    wavfile.setframerate(SAMPLE_RATE)

    for sample in windowed_sinc(SAMPLE_RATE * DURATION, FREQUENCY / SAMPLE_RATE):
        wavfile.writeframes(struct.pack("<h", int(sample * 32767)) * 2)