Adding raised cosine and sqrt raised cosine filter templates

Author: RGerzaguet

src/DigitalComm.jl

@@ -53,6 +53,11 @@ include("Channel/addCFO.jl")
 export addCFO
 export addCFO!
 
+# --- Raised cosine filters
+include("raisedCosine.jl")
+export raisedCosine
+export sqrtRaisedCosine
+
 
 # ---------------------------------------------------- 
 # --- Function definition  

src/raisedCosine.jl

@@ -0,0 +1,73 @@
+"""   
+Returns the Finite Impulse Response of a Raised Cosine (RC) filter.	The filter is defined by its span (evaluated in number of symbol N), its Roll-Off factor and its oversampling factor. The span corresponds to the number of symbol affected by filter before and after the center point.\n
+Output is a Vector{Float64} array of size L= 2KN+1 \n
+SRRC definition is based on [1]	 \n
+[1]	 3GPP TS 25.104 V6.8.0 (2004-12). http://www.3gpp.org/ftp/Specs/archive/25_series/25.104/25104-680.zip \n
+ Syntax \n
+		h	= raisedCosine(N,beta,ovS)
+Input parameters \n
+- N	  : Symbol span (Int16)
+- beta  : Roll-off factor (Float64)
+- ovS	  : Oversampling rate (Int16)
+"""
+function raisedCosine(N,beta,ovS)
+	# --- Final size of filter
+	nbTaps	= 2 * N * ovS + 1;
+	# --- Init output
+	h			= zeros(Float64,nbTaps);
+	counter		= 0;
+	# --- Iterative SRRC definition
+	for k = -N*ovS : 1 : N*ovS
+		counter		 = counter + 1;
+		if k == 0
+			## First singular point at t=0
+			h[counter]  = 1;#(1-beta) + 3*beta/pi;
+		elseif abs(k) == ovS / (2*beta);
+			## Second possible singular point
+			h[counter]  = pi/4*sin(pi/(2beta))/(pi/(2beta));
+		else
+			## Classic SRRC formulation (see [1])
+			h[counter]	= sin(pi*k/ovS)/(pi*k/ovS) * cos(pi*beta*k/ovS)/(1- 4beta^2*(k/ovS)^2);
+		end
+	end
+	return h
+end
+
+
+"""
+Returns the Finite Impulse Response of a Square Root Raised Cosine (SRRC) filter. \n
+The filter is defined by its span (evaluated in number of symbol N), its Roll-Off factor and its oversampling factor. The span corresponds to the number of symbol affected by filter before and after the center point.\n
+Output is a Vector{Float64} array of size L= 2KN+1\n
+SRRC definition is based on [1]\n
+[1]	 3GPP TS 25.104 V6.8.0 (2004-12). http://www.3gpp.org/ftp/ Specs/archive/25_series/25.104/25104-680.zip\n
+Syntax\n
+h	= sqrtRaisedCosine(N,beta,ovS) \n
+Input parameters \n
+- N	  : Symbol span (Int16)
+- beta  : Roll-off factor (Float64)
+- ovS	  : Oversampling rate (Int16)
+"""
+function sqrtRaisedCosine(N,beta,ovS)
+	# --- Final size of filter
+	nbTaps	= 2 * N * ovS + 1;
+	# --- Init output
+	h			= zeros(Float64,nbTaps);
+	counter		= 0;
+	# --- Iterative SRRC definition
+	for k = -N*ovS : 1 : N*ovS
+		counter		 = counter + 1;
+		if k == 0
+			## First singular point at t=0
+			h[counter]  = (1-beta) + 4*beta/pi;
+		elseif abs(k) == ovS / (4*beta);
+			## Second possible singular point
+			h[counter]  = beta/sqrt(2)*( (1+2/pi)sin(pi/(4beta))+(1-2/pi)cos(pi/(4beta)));
+		else
+			## Classic SRRC formulation (see [1])
+			h[counter]  = ( sin(pi*k/ovS*(1-beta)) + 4beta*k/ovS*cos(pi*k/ovS*(1+beta))) / (pi*k/ovS*(1- (4beta*k/ovS)^2) );
+		end
+	end
+    # --- Max @ h[0]
+    h   = h ./ maximum(h)
+	return h
+end

test/runtests.jl

@@ -18,9 +18,11 @@ include("test_hardConstellation.jl");
 # Symbol demapper 
 include("test_symbolDemapper.jl");
 
-
 # AWGN 
 include("test_addNoise.jl");
 
 # Test Waveforms 
 include("test_waveforms.jl");
+
+# Test filters 
+include("test_filters.jl")

test/test_filters.jl

@@ -0,0 +1,44 @@
+# ---------------------------------------------------- 
+# --- Import modules  
+# ---------------------------------------------------- 
+using DigitalComm 
+using DSP 
+using Test
+# ---------------------------------------------------- 
+# --- Tests 
+# ---------------------------------------------------- 
+println("Tests for filters");
+@testset "Raised Cosine filter test" begin 
+    # Create the vector 
+    h = raisedCosine(12,0.5,16)
+    # Check type 
+    @test h isa Vector{Float64}
+    # Check size 
+    sH = 12*16*2+1
+    @test length(h)== sH
+    # Check it is 1 in the middle 
+    @test h[1+ (sH-1)÷2] == 1
+    # Check Nyquist criterion
+    for n ∈ 0 : 11 
+        @test ≈(h[1 + n*16],0,atol=1e-8)
+    end
+end
+
+@testset "Raised Cosine filter test" begin 
+    # Create the vector 
+    h = sqrtRaisedCosine(12,0.5,16)
+    # Check type 
+    @test h isa Vector{Float64}
+    # Check size 
+    sH = 12*16*2+1
+    @test length(h)== sH
+    # Check it is 1 in the middle 
+    @test h[1+ (sH-1)÷2] == 1
+    # Check Nyquist criterion
+    # sqrt is not a Nyquist filter but h*h is !
+    p = conv(h,h)
+    p = p /maximum(p)
+    for n ∈ 0 : 2*11 
+        @test ≈(p[1 + n*16],0,atol=1e-4)
+    end
+end