docs for synthesis added + other minor updates

Documentation for the function `STFT.synthesis` has been created.
Some minor updates in the documentation for `STFT.analysis` function.

src/STFT.jl

@@ -24,17 +24,17 @@ using Short-Time Fourier Transform given by
 
 where ``s`` and ``\\omega`` denotes segment index and angular frequency
 respectively, ``\\mathrm{w}[n]`` is a discrete time-domain signal of analysis
-window, ``H`` is nonnegative integer value that determine number of
+window, and ``H`` is nonnegative integer value that determine number of
 samples between two consecutive signal segments (also known as `hop`).
 
 
 # Parameters
 
 - `x` - An array containing samples of a discrete time-domain signal.
-- `w` - An array containing samples of a discrete time-domain window.
+- `w` - An array containing samples of a discrete time-domain analysis window.
 - `L` - An overlap in samples between two consecutive segments.
         Default value is `0`.
-- `N` - A number of discrete frequency bins used in DFT computation.
+- `N` - A number of discrete frequency bins to be used in the DFT computation.
         Default value is `length(w)`.
         If `N < length(w)`, then `N=length(w)` is enforced to avoid loss of
         information.
@@ -103,6 +103,77 @@ end
 
 
 
+"""
+    synthesis(X::Matrix, w::Vector, L=0, N=length(w)) -> Vector
+
+Syntesise discrete time-domain signal ``y[n]`` from STFT-domain signal
+``Y_w[sH, n]``.
+An arbitrary STFT-domain signal ``Y_w[sH, n]``, in general, is not a valid STFT
+in the sense that there is no discrete time-domian signal whoes STFT is given
+by ``Y_w[sH, n]`` [1].
+As result, time-domain signal must be estimated using following formula [1]:
+```math
+y[n] = \\frac{
+    \\sum\\limits_{s=-\\infty}^{+\\infty} w[n - sH] \\ y_w[sH, n]
+}{
+    \\sum\\limits_{s=-\\infty}^{+\\infty} w^2[n - sH]
+},
+```
+where ``w[n]`` is time-domain signal of analysis window,
+``y_w[sH, n]`` is time-domain representation of ``Y_w[sH, n]``,
+and ``H`` is nonnegative integer value that determine number of
+samples between two consecutive signal segments (also known as `hop`).
+
+# Parameters
+
+- `X` - An matrix containing samples of a discrete STFT-domain signal.
+- `w` - An array containing samples of a discrete time-domain analysis window.
+- `L` - An overlap in samples between two consecutive segments.
+        Default value is `0`.
+- `N` - A number of discrete frequency bins to be used in the inverse DFT
+        computation. Default value is `length(w)`.
+        If `N < length(w)`, then `N=length(w)` is enforced to avoid loss of
+        information.
+
+# Returns
+
+- `x` - A real-valued vector containing estimated time-domain signal.
+
+# Note
+
+1. Relation between ``H`` and ``L`` is given as ``H = W - L`` where ``W`` is
+   a length of a window.
+2. This function supports only synthesis of real-valued signals from
+   one-sided STFT-domain signal.
+3. Synthesised time-domain signal might be shorter than analysed one,
+   since only whole segments are analysed.
+
+
+# Example
+```julia
+import STFT
+
+x = rand(100)   # Generate mock signal
+W = 64          # Window length
+w = ones(W)     # Rectangular analysis window
+H = 4           # Hop
+L = W - H       # Overlap
+
+X  = STFT.analysis(x, w, L)  # Analysis
+xr = STFT.synthesis(X, w, L) # Synthesis
+```
+
+# References
+1. D. Griffin and J. Lim, “Signal estimation from modified short-time
+   Fourier transform,” IEEE Transactions on Acoustics, Speech, and
+   Signal Processing, vol. 32, no. 2, pp. 236–243, Apr. 1984,
+   doi: 10.1109/TASSP.1984.1164317.
+   \\[[IEEE Xplore](https://ieeexplore.ieee.org/abstract/document/1164317),
+   [pdf](https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.331.7151&rep=rep1&type=pdf)\\]
+"""
+function synthesis()
+end
+
 function synthesis(
     X::AbstractMatrix{<:Complex},
     w::AbstractVector{<:Real},
@@ -121,9 +192,9 @@ function synthesis(
 
     for s ∈ 1:S
         ss = (s-1)*H # Segment start
-        for k = 1:W
-            xn[ss+k] += xs[k, s] * w[k]
-            xd[ss+k] += w²[k]
+        for n = 1:W
+            xn[ss+n] += xs[n, s] * w[n]
+            xd[ss+n] += w²[n]
         end
     end
     xn ./ xd # Normalize