onepole~

Discussion

The standard difference equation for this filter is

y(n) = a_{0} x(n) + b_{1} y(n-1)
Where

b_{1} = 1 - a_{0}

which can be factored down to

y(n) = y(n-1) + a_{0}[ x(n) - y(n-1) ]

As the value of the a_{0} coefficient is lowered (b_{1} increases) the input will be increasingly smoothed and the effective cutoff frequency (f_c) lowered. Calculating the a_0 coefficient from the f_c cutoff frequency is performed with the equation

a_{0} = sin(f_c * (pi/nyquist))

where f_s is the sampling frequency and f_c the cutoff frequency expressed in Hertz. onepole~ is a more efficient implementation of a biquad~ object with the following coefficients:

a_{0} &= a_{0}
a_{1} &= 0
a_{2} &= 0
b_{1} &= -b_{1}
b_{2} &= 0
Note the sign flip for b_{1} as biquad uses flipped signs for the feedback coefficients.