Channel Identification Machines

Figure 12

Channel identification in a SISO [Filter]-[Ideal IAF] circuit using signals from the Paley-Wiener space Ξ. (a) In contrast to Figure 6, input signals 𝑢^𝑖∈Ξ, 𝑖=1,…,5. (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 38 spikes in response to all 5 input signals. (e) The identified impulse response of the filter 𝒫ℎ^∗ (red) is shown together with the original filter ℎ (dashed black) and its projection 𝒫ℎ (blue). The MSE between 𝒫ℎ^∗ and 𝒫ℎ is −71.1 dB. (f)–(h) Fourier amplitude spectra of 𝐾, ℎ, and 𝒫ℎ^∗. In contrast to Figure 6, 𝐾 and 𝒫ℎ^∗ do not exhibit a discrete (line) spectrum. Again, 𝒫ℎ^∗∈Ξ but ℎ∉Ξ.