Ejemplos de código en Julia de la Guía 1

Código auxiliar

# Cargo un par de paquetitos básicos
using DSP, Plots
# Y armo un par de funciones auxiliares
stem(args...; kwargs...) = sticks(args...; 
  																marker=:circle, 
  																leg=false, 
  																kwargs...)
# Delta
d(n) = n == 0 ? 1. : 0. 
# Escalón
u(n) = n >= 0 ? 1. : 0. 
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u (generic function with 1 method)

1) Graficar

formula not implemented
let
  ns = -4:4
  x  = -2 .* d.(ns .+ 2)
  
  stem(ns, x; 
    xaxis="n", 
    title="a) -2d(n+2)")
end
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formula not implemented
let
  ns = -3:3
  x  = 2.0 .^ ns .* u.(ns)
  
  stem(ns, x; 
    xaxis="n", 
    title="b) 2^n*u(n)")
end
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formula not implemented
let
  ns = -3:3
  x  = 2.0 .^ -ns .* u.(ns)
  
  stem(ns, x; 
    xaxis="n", 
    title="c) 2^-n*u(n)")
end
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formula not implemented
let
  ns = -4:4
  x  = 2.0 .^ -ns .* u.(-ns)
  
  stem(ns, x; 
    xaxis="n", 
    title="...")
end
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formula not implemented
let
  ns = 0:11
  x  = cos.(pi/3 .* ns) .* u.(ns .- 2)
  
  stem(ns, x; 
    xaxis="n", 
    title="...")
end
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2) Corroborar sumas

sum(exp(-im*π/2*n) for n in 0:9)
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1.0-1.0im
sum(exp(im*π/2*n) for n in -2:7)
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-1.0-1.0im
sum((1/2)^n * exp(im*π/2*n) for n in 0:9)
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0.800781+0.400391im
sum(cos(π/2*n) for n in 0:9)
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1.0

4) Pulso rectangular

Supongamos inline_formula not implemented y inline_formula not implemented

let
  N  = 10
  A  = 7
  
  ns = -5:15
  xs = A .* (u.(ns) - u.(ns .- N))
  
  stem(ns, xs)
end
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10) Submuestreo y sobremuestreo

sub2(x)  = x[1:2:end]
function sobre2(x)
  out = zeros(2 * length(x))
  out[1:2:end] = x
  
  return out
end
# Ejemplo
x = cos.(0:0.3:10)
stem(x)
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stem(sub2(x))
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stem(sobre2(x))
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Runtimes (1)