Discusses Fourier Transform’s in signal processing, physics, and engineering, where it converts time-domain functions into frequency-domain representations. Explains the Inverse Fourier Transform and Discrete Fourier Transform (DFT) for discrete signals. It also covers the Fast Fourier Transform (FFT), an efficient algorithm for polynomial multiplication, detailing the key steps involved in its execution and its overall time complexity of O(n log n + n). Explains how Numpy handles FFT operations with functions like numpy.fft.fft for forward and numpy.fft.ifft for inverse transformations.

Addresses the challenges of structured vs. unstructured data, and introduces the Bag of Words model for feature representation. Explain why each document can be represented as a point in a d-dimensional feature space.

Language modeling in NLP is essential for applications like autocomplete and translation, focusing on text fluency by predicting the next word based on context. It utilizes models such as unigram, bigram, and n-gram, with effective modeling requiring efficient context management through fixed windows. Key challenges include representing history for accurate predictions, while neural language models and techniques like LSTM enhance performance by managing memory and context in sequences.