Channel Identification Machines

Figure 6

Channel identification in a SISO [Filter]-[Ideal IAF] circuit using multiple I/O pairs. (a) Input signals 𝑢¹,…,𝑢⁴ are bandlimited to 100 Hz. The order of the space 𝐿=20. (b) Biased output of the filter 𝑣¹(𝑡)+𝑏 in response to the stimulus 𝑢¹. (c) The filter output in (b) is integrated by an ideal IAF neuron. (d) The neuron generated a total of 48 spikes in response to all 4 input signals. (e) The identified impulse response 𝒫ℎ^∗ (red) is shown together with the original filter ℎ (dashed black) and its projection 𝒫ℎ (blue). The MSE between 𝒫ℎ^∗ and 𝒫ℎ is −73.3 dB. (f)–(h) Fourier amplitude spectra of 𝐾, ℎ and 𝒫ℎ^∗. Note that supp(ℱ𝐾)=[−Ω,Ω]=supp(ℱ𝒫ℎ^∗) but supp(ℱℎ)⊃[−Ω,Ω]. In other words, 𝒫ℎ^∗∈ℋ but ℎ∉ℋ.