Convenience method for state-space realization of FIR system

Author: olof3

src/demo_systems.jl

@@ -123,4 +123,21 @@ function woodberry()
 end
 
 
+
+"""
+    `ssfir(c [,Ts=1]) -> sysd`
+
+Returns a (discrete-time) state-space realization `sysd` of a
+finite-impulse response (FIR) system with impulse response `c`.
+"""
+function ssfir(c::AbstractVector{T}, Ts=1) where T
+    n = length(c)-1
+    if n == 0
+        return ss(c[1], Ts)
+    end
+    A = diagm(-1=>ones(T, n-1))
+    B = [1; zeros(T,n-1)]
+    ss(A, B, transpose(c[2:end]), c[1], Ts)
+end
+
 end

test/test_demo_systems.jl

@@ -36,4 +36,26 @@ sys = ssrand(2,2,5,proper=false,stable=true, Ts=0.5)
 sys = ssrand(2,2,5,proper=false,stable=false, Ts=0.5)
 @test !isstable(sys)
 
+
+
+c = [2.5]
+sysd = DemoSystems.ssfir(c)
+y = impulse(sysd, 10)[1]
+@test y[1] == c[1]
+@test y[2:11] == zeros(10)
+
+
+c = [0.1, 2.5]
+sysd = DemoSystems.ssfir(c)
+y = impulse(sysd, 10)[1]
+@test y[1:2] == c[1:2]
+@test y[3:11] == zeros(9)
+
+
+c = [1,2,5,3]
+sysd = DemoSystems.ssfir(c)
+y = impulse(sysd, 10)[1]
+@test y[1:4] == c
+@test y[5:11] == zeros(7)
+
 end