Channel Identification Machines

Figure 13

Noisy channel identification in a SISO [Filter]-[Ideal IAF] circuit using multiple I/O pairs. (a) Input signals 𝑢¹,𝑢² are bandlimited to 25 Hz. The order of the space 𝐿=5. (b) Biased output of the filter 𝑣¹(𝑡)+𝑏 in response to the stimulus 𝑢¹. (c) Thresholds are random with 𝛿_𝑘∼𝒩(𝛿,(0.1𝛿)²). (d) The neuron produced a total of 26 spikes in response to 2 stimuli. (e) The optimal estimate 𝒫ℎ^∗ (red) is shown together with the original filter ℎ (dashed black) and its projection 𝒫ℎ (blue). Note that the MSE between 𝒫ℎ^∗ and 𝒫ℎ is −31.8 dB. (f)–(h) Fourier amplitude spectra of 𝐾, ℎ and 𝒫ℎ^∗. As before, supp(ℱ𝐾)=[−Ω,Ω] = supp(ℱ𝒫ℎ^∗) but supp(ℱℎ)⊃[−Ω,Ω]. In other words, 𝒫ℎ^∗∈ℋ but ℎ∉ℋ.