Show that X̂ cW ( f ) is more noisy but less distorted than X̂ W ( f ), and that X̂c W, 2 ( f ) is less noisy but more distorted than X̂ W ( f ): Let 𝐠 and ̃𝐠 be, respectively, analysis and...

Show that X̂_cW( f ) is more noisy but less distorted than X̂_W( f ), and that X̂c_W,
2( f ) is less noisy but more distorted than X̂_W( f ):

Let 𝐠 and ̃𝐠 be, respectively, analysis and synthesis windows of the STFT. Show that the condition for exact reconstruction with the inverse STFT is

Show that for a given analysis window 𝐠 of length L > R, the synthesis window of a minimal norm that satisfies the condition of exact reconstruction is given by