# conv

conv(u,v)

Convolution of two vectors. Uses FFT algorithm.

## Examples

In the Julia programming language, the function `conv(u, v)` is used to perform the convolution of two vectors `u` and `v`. It utilizes the Fast Fourier Transform (FFT) algorithm for efficient computation.

``````julia> conv([1, 2, 3], [4, 5, 6])
5-element Array{Int64,1}:
4
13
28
27
18``````

Here are some common examples of using the `conv` function:

1. Convolution of two audio signals:

``````julia> signal1 = [0.2, 0.5, 0.8, 0.2, 0.3];
julia> signal2 = [0.1, 0.3, 0.5];
julia> conv(signal1, signal2)
7-element Array{Float64,1}:
0.02
0.09
0.23
0.38
0.51
0.41
0.24``````

This example shows the convolution of two audio signals represented as arrays.

2. Applying a filter to a time series:
``````julia> timeSeries = [10, 20, 30, 40, 50];
julia> filter = [0.5, 0.25, 0.1];
julia> conv(timeSeries, filter)
7-element Array{Float64,1}:
5.0
8.75
12.5
15.25
18.0
13.0
5.0``````

This example demonstrates the application of a filter to a time series using convolution.

Common mistake example:

``````julia> conv([1, 2, 3], [4, 5])
ERROR: DimensionMismatch("vectors must have same length")``````

In this example, the vectors `u` and `v` provided to `conv` have different lengths, resulting in a `DimensionMismatch` error. Ensure that the input vectors have the same length before using the `conv` function.