How to Reduce Speech Feature Dimensions?
You have one feature vector per frame. The collection of feature vectors for all the frames in the training data form a matrix. Since this is training data, you know the true class for each frame. Use this matrix and the training data labels to build your LDA matrix. Alternatively, just use this matrix (without the labels) to find the PCA matrix.

Now you use this matrix to reduce the dimensionality of the feature vector for each frame in your test data when you're doing the speech recognition.

PCA doesn't produce less variant features. I think what you meant to say was that the features are less correlated with each other. This is called whitening and it can help some classifiers better learn from the training data.