Dimensionality Reduction : Does PCA really improve classification outcome?

I have come across a couple of resources about dimensionality reduction techniques. This topic is definitively one of the most interesting ones, and it is great to think that there are algorithms able to reduce the number of features by choosing the most important ones that still represent the entire dataset. One of the advantages pointed out by authors is that these algorithms can improve the results of a classification task. In this post, I am going to verify this statement using a Principal Component Analysis ( PCA) to try to improve the classification performance of a neural network over a dataset. Does PCA really improve classification outcome?