bandlimited_interpolation.rb

# Bandlimited interpolation simulation, as described by Eq 1 of
# https://ccrma.stanford.edu/~jos/resample/Theory_Ideal_Bandlimited_Interpolation.html

Fs = 44100.0 # sampling rate
Ts = 2.26757369614512e-05 # sampling interval (1/Fs)
 
def interp(samps, t)
  (0...samps.size).inject(0) { |sum, n|
    sum + samps[n] * hs(t - n * Ts)
  }
end
 
def hs(t)
  sinc(Fs * t)
end
 
def sinc(t)
  if t.zero? then 1.0
  else
    Math.sin(Math::PI * t) / (Math::PI * t)
  end
end
 
# A continuous-time 440 Hz sine wave
def x(t)
  Math.sin(2.0 * Math::PI * 440.0 * t)
end

# Sample 1sec of a continuous function
def samp
  Array.new(Fs) { |n| yield(n*Ts) }
end

# 440 Hz sine wave sampled at 44.1 kHz
sine = samp { |t| x(t) }

# Randomly sample continuous function and its reconstruction from a discrete signal
puts "T\t\tx(T)\t\tinterp(samp(x), T)\tdelta"
1000.times do
  t  = rand()
  xt = x(t)
  it = interp(sine, t)
  puts "% .4fsec\t% .4e\t% .4e\t\t%.4e" % [t, xt, it, (xt-it).abs]
end

# Compare sampled sine wave with reconstruction at sampling points
(0...Fs).each do |n|
  puts "%.7f\t%.7f" % [x(n/Fs), interp(sine, n/Fs)]
end