Template

# Cargo paquetitos

using DSP, FFTW, Statistics, WAV

function wavread_mono(file)

  x, sr = wavread(file)

  return mean(x; dims=2)[:], sr

end

# Y armo un par de funciones auxiliares

stem(args...; kwargs...) = sticks(args...; 

  																marker=:circle, 

  																leg=false, 

  																kwargs...)

stem!(args...; kwargs...) = sticks!(args...; 

  																marker=:circle, 

  																leg=false, 

  																kwargs...)

zeropolegain(pr) = DSP.ZeroPoleGain(pr)

zeropolegain(z, p, g) = DSP.ZeroPoleGain(z, p, g)

polynomialratio(zpg) = DSP.PolynomialRatio(zpg)

function polynomialratio(b, a)

  n = max(length(a), length(b))

  return DSP.PolynomialRatio(padright(b, n), padright(a, n))

end

getpoles(zpg) = DSP.ZeroPoleGain(zpg).p

getzeros(zpg) = DSP.ZeroPoleGain(zpg).z

getgain(zpg) = DSP.ZeroPoleGain(zpg).k

getnumcoefs(pr) = trimlastzeros!(reverse(DSP.PolynomialRatio(pr).b.coeffs))

getdencoefs(pr) = trimlastzeros!(reverse(DSP.PolynomialRatio(pr).a.coeffs))

function trimlastzeros!(a)

  !iszero(a[end]) && return a

  pop!(a)

  return trimlastzeros!(a)

end

DSP.filt(zpg::DSP.ZeroPoleGain, r...; kwargs...) = filt(polynomialratio(zpg), r...; kwargs...)

function zplane(zs, ps; kwargs...)

	scatter(real.(zs), imag.(zs);

		  marker = (:black, :circle), label="Cero", kwargs...)

	scatter!( real.(ps), imag.(ps);

	  	marker = (:red, :xcross), label="Polo", kwargs...)  

  ts = range(0,stop=2pi;length=100)

  plot!(cos.(ts), sin.(ts); aspect_ratio = 1, kwargs...)

end

zplane(pr::DSP.PolynomialRatio; kwargs...) = zplane(DSP.ZeroPoleGain(pr); kwargs...)

# Delta

d(n) = n == 0 ? 1. : 0. 

# Escalón

u(n) = n >= 0 ? 1. : 0. 

using Plots

Plots.default(:legend, false)

# Pad vector with zeros on the right until its length is `n`

padright(x, n) = copyto!(zeros(eltype(x), n), x)

"""

Función módulo pero con offset (opcional)

Manda a `t` al intervalo [from, from+length)

sumándole o restándole algún múltiplo de `len`

"""

cshift(t, len, from=0) = mod(t - from, len) + from

	# Espectrograma

	using IterTools

	function stft(x; overlap, window, nfft, rest...)

	  nwin = length(window)

	  @assert overlap < nwin

	  res = [ fft(padright(xseg .* window, nfft))

		for xseg in partition(x, nwin, nwin - overlap)]

	  return [ res[i][j] for j in 1:nfft, i in eachindex(res)]

	end

	specplot(x::AbstractMatrix; kwargs...) = 

		@error "You are entering a Matrix (2D Array). I need a Vector (1D Array)."

	function specplot(x::AbstractVector;

		  fs=1,

		  onesided=false,

		  xaxis="Tiempo (s)",

		  yaxis="Frecuencia (Hz)",

		  window=hamming(div(length(x), 16)),

		  overlap=0.5,

		  nfft=length(window),

		  kws...)

		window isa Integer && (window = rect(window))

		overlap isa AbstractFloat && (overlap = round(Int, length(window) * overlap))

		mat = stft(x; overlap=overlap, window=window, nfft=nfft)

		fmax = fs

		if onesided

		  mat = mat[1:div(size(mat, 1) + 2, 2), :]

		  fmax = fs/2

		end

	  toffset = length(window) / 2fs

	  times = range(toffset; length=size(mat, 2), stop=length(x)/fs - toffset)

	  freqs = range(0; length=size(mat, 1), stop=fmax)

		# Reubico las frecuencias negativas arriba de todo

	  if !onesided

		freqs = cshift.(freqs, fs, -fs/2)

		ord   = sortperm(freqs)

		mat   = mat[ord, :]

		freqs = freqs[ord]

	  end

		return heatmap(times, freqs, log.(abs.(mat) .+ eps());

			  xaxis=xaxis, yaxis=yaxis,

			  seriescolor=:bluesreds, legend=true, kws...)

	 return times, freqs, mat

	end

	function specplot(x :: AbstractVector{<:AbstractFloat}; kws...)

		return specplot(convert.(Complex, x); onesided=true, kws...)

	end