Simulation of the continuous measurement of spatial room impulse responses

[narahahn]

Simulation of the captured signal

• Define sound source position
• Define a microphone movement (radius, angular speed, etc)
• The angular position of the microphone phi (length of L)
• Gerenate a perfect sequence p (length N)
• Compute the captured signal s, which has the same length L

System identification

• Select a set of target positions phi_target (length K) at which the impulse responses are to be computed
• Decompose the captured signal into N sub-signals, where the i-th signal is s[i::N]
• The i-th signal 's_i' (i=0,...,N-1) corresponds to angular positions phi[i::N]
• For each target angle phi_target[k] (k=0,...,K-1), reconstruct the original sound field y by using spatial interpolation
• The interpolation will look like this:
  y[i] = spatial_interpolation(s_i, phi_i, phi_target[k])
  So you get the i-th sample of the sound field at phi_target[k]
• The corresponding impulse response h is then given as the circular cross correlation of y and the perfect sequence p
h = cross_correlation(y, p)
• The overall structure will look more or less like this:

impulse_responses = np.zeros((N,K))
for k in range(K):
	y = np.zeros(N)
	for i in range(N):
		s_i = s[i::N]
		phi_i = phi[i::N]
		y[i] = spatial_interpolation(phi_i, s_i, phi_target[k])
	impulse_responses[:, k] = circular_cross_correlation(y, p)

• You should implement the function spatial_interpolation

Extension to MISO case

• Define multiple microphone loudspeaker positions (M)
• Generate perfect sequences. The period has to be M*N. Apply a time-shift of m*N to the m-th signal
• Compute the superimposed signal (sum up)
• The same procedure as above
• This time, circular_cross_correlation(y, p) will have a length of M*N. Each block of N samples correspond to the m-th impulse response.