[#852] [#852] Fix for Julia 1D convolution (#854)

* [#852] [#853] Fix for Julia 1D convolution

* fixing line numbers for jie's PR

Co-authored-by: James Schloss <jrs.schloss@gmail.com>

Author: jiegillet

contents/convolutions/1d/1d.md

@@ -53,7 +53,7 @@ With this in mind, we can almost directly transcribe the discrete equation into
 
 {% method %}
 {% sample lang="jl" %}
-[import:29-48, lang:"julia"](../code/julia/1d_convolution.jl)
+[import:27-46, lang:"julia"](../code/julia/1d_convolution.jl)
 {% endmethod %}
 
 The easiest way to reason about this code is to read it as you might read a textbook.
@@ -184,30 +184,30 @@ Here it is again for clarity:
 
 {% method %}
 {% sample lang="jl" %}
-[import:29-48, lang:"julia"](../code/julia/1d_convolution.jl)
+[import:27-46, lang:"julia"](../code/julia/1d_convolution.jl)
 {% endmethod %}
 
 Here, the main difference between the bounded and unbounded versions is that the output array size is smaller in the bounded case.
 For an unbounded convolution, the function would be called with a the output array size specified to be the size of both signals put together:
 
 {% method %}
 {% sample lang="jl" %}
-[import:60-61, lang:"julia"](../code/julia/1d_convolution.jl)
+[import:58-59, lang:"julia"](../code/julia/1d_convolution.jl)
 {% endmethod %}
 
 On the other hand, the bounded call would set the output array size to simply be the length of the signal
 
 {% method %}
 {% sample lang="jl" %}
-[import:63-64, lang:"julia"](../code/julia/1d_convolution.jl)
+[import:61-62, lang:"julia"](../code/julia/1d_convolution.jl)
 {% endmethod %}
 
 Finally, as we mentioned before, it is possible to center bounded convolutions by changing the location where we calculate the each point along the filter.
 This can be done by modifying the following line:
 
 {% method %}
 {% sample lang="jl" %}
-[import:37-37, lang:"julia"](../code/julia/1d_convolution.jl)
+[import:35-35, lang:"julia"](../code/julia/1d_convolution.jl)
 {% endmethod %}
 
 Here, `j` counts from `i-length(filter)` to `i`.
@@ -239,7 +239,7 @@ In code, this typically amounts to using some form of modulus operation, as show
 
 {% method %}
 {% sample lang="jl" %}
-[import:4-27, lang:"julia"](../code/julia/1d_convolution.jl)
+[import:4-25, lang:"julia"](../code/julia/1d_convolution.jl)
 {% endmethod %}
 
 This is essentially the same as before, except for the modulus operations, which allow us to work on a periodic domain.

contents/convolutions/code/julia/1d_convolution.jl

@@ -13,9 +13,7 @@ function convolve_cyclic(signal::Array{T, 1},
 
     for i = 1:output_size
         for j = 1:output_size
-            if (mod1(i-j, output_size) <= length(filter))
-                sum += signal[mod1(j, output_size)] * filter[mod1(i-j, output_size)]
-            end
+            sum += get(signal, mod1(j, output_size), 0) * get(filter, mod1(i-j, output_size), 0)
         end
 
         out[i] = sum
@@ -57,8 +55,8 @@ function main()
     normalize!(x)
     normalize!(y)
 
-    # full convolution, output will be the size of x + y
-    full_linear_output = convolve_linear(x, y, length(x) + length(y))
+    # full convolution, output will be the size of x + y - 1
+    full_linear_output = convolve_linear(x, y, length(x) + length(y) - 1)
 
     # simple boundaries
     simple_linear_output = convolve_linear(x, y, length(x))