Cover more tests

Signed-off-by: ErikQQY <[email protected]>

Author: ErikQQY

docs/src/frft.md

@@ -6,13 +6,14 @@ Pages = ["frft.md"]
 
 ## Definition
 
-While we are already familiar with the ordinary Fourier transform, which is defined by the integral of the product of the original function and a kernel function ``e^{-2\pi ix\xi}​``:
+While we are already familiar with the Fourier transform, which is defined by the integral of the product of the original function and a kernel function ``e^{-2\pi ix\xi}​``:
 
 ```math
 \hat{f}(\xi)=\mathcal{F}[f(x)]=\int_{-\infty}^\infty f(x)e^{-2\pi ix\xi}dx
 ```
 
 The Fractional Fourier transform has the similar definition:
+
 ```math
 \hat{f}(\xi)=\mathcal{F}^{\alpha}[f(x)]=\int_{-\infty}^\infty K(\xi,x)f(x)dx
 ```

docs/src/index.md

@@ -34,4 +34,4 @@ I would like to express gratitude to
 **FractionalTransforms.jl** is built upon the hard work of many scientific researchers, I sincerely appreciate what they have done to help the development of science and technology.
 
 !!! info "WIP"
-		FractionalTransforms.jl is under heavy construction, some API or docs might change a lot.
+	FractionalTransforms.jl is under heavy construction, some API or docs might change a lot.

src/frft.jl

@@ -1,4 +1,5 @@
-using DSP, LinearAlgebra, ToeplitzMatrices, FFTW
+using DSP: conv
+using LinearAlgebra, ToeplitzMatrices, FFTW
 
 """
     frft(signal, α)
@@ -78,13 +79,13 @@ function frft(signal, α)::Vector{ComplexF64}
 
     y = y[2*M+1:end-2*M]
     y = y[1:3:end]
-    y= @. exp(-im*(pi*sign(sin(ϕ))/4-ϕ/2))*y
+    y = @. exp(-im*(pi*sign(sin(ϕ))/4-ϕ/2))*y
 
     return y
 end
 
 function freq_shear(x, c)
-    x=x[:]
+    x = x[:]
     N = length(x)
     if rem(N, 2) == 0
         error("Signal must be odd")
@@ -121,17 +122,17 @@ end
 
 ```Sinc interpolation``` of **signal** at rate **rate**.
 
-For more details, please refer to [Whittaker-Shannon interpolation](https://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_formula)
+For more details, please refer to [Whittaker-Shannon interpolation](https://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_formula).
 """
 function sinc_interp(x, rate)
-    x=x[:]
-    N=length(x)
-    M=rate*N-rate+1
+    x = x[:]
+    N = length(x)
+    M = rate*N - rate + 1
 
     y = zeros(ComplexF64, M)
     @views y[1:rate:M] = x
 
     h =  sinc.(collect(-(N-1-1/rate):1/rate:(N-1-1/rate)))
     out = conv(y, h)
-    out=out[(rate*N-rate):(end-rate*N+rate+1)]
+    out = out[(rate*N-rate):(end-rate*N+rate+1)]
 end

test/frft.jl

@@ -4,4 +4,16 @@ using Test
 @testset "Test FRFT" begin
     @test isapprox(real(frft([1,2,3], 0.5)), [0.100464613588213, 3.07460010423315, 1.31566432887283], atol=1e-5)
     @test isapprox(imag(frft([1,2,3], 0.5)), [-0.259409480977277, 0.199349381540632, -0.93645356561191], atol=1e-5)
+end
+
+@testset "Test FRFT auxillary functions" begin
+    @testset "Test Sinc Interpolation" begin
+        @test isapprox(real(sinc_interp([1, 2, 3], 3)), [1.0, 1.1577906803857638, 1.4472383504822042, 2.0, 2.6877283651812367, 3.1425747039042147, 3.0]; atol=1e-5)
+        @test isapprox(imag(sinc_interp([1, 2, 3], 3)), [-4.0696311822644287e-17, -2.4671622769447922e-17, -2.522336560207922e-16, -3.331855648569948e-17, 0.0, 1.9624582529744518e-17, 3.331855648569948e-17]; atol=1e-5)
+    end
+
+    @testset "Test Frequency Shear" begin
+        @test isapprox(real(freq_shear([1, 2, 3], 3)), [0.0707372016677029, 2.0, 0.2122116050031087]; atol=1e-5)
+        @test isapprox(imag(freq_shear([1, 2, 3], 3)), [0.9974949866040544, 0.0, 2.9924849598121632]; atol=1e-5)
+    end
 end