A Supervised Learning Method for the Design of Linear Phase FIR Digital Filter Using Keras In this paper, a supervised learning method for the design of linear phase FIR digital filter using Keras is presented. First, the design problem of the linear phase finite impulse response (FIR) digital filter is transformed to a supervised learning problem. Then, the optimizers in Keras framework are used to determine the filter coefficients by minimizing the mean squared error (MSE) loss function. The widelyused optimizers include adaptive moments (Adam) algorithm and stochastic gradient descent (SGD) with momentum algorithm. Finally, the numerical design examples of lowpass and highpass FIR digital filters are demonstrated to show the usefulness of the supervised learning method with Keras framework.

Improving Machine Hearing on Limited Data Sets Convolutional neural network (CNN) architectures have originated and revolutionized machine learning for images. In order to take advantage of CNNs in predictive modeling with audio data, standard FFTbased signal processing methods are often applied to convert the raw audio waveforms into an imagelike representations (e.g. spectrograms). Even though conventional images and spectrograms differ in their feature properties, this kind of preprocessing reduces the amount of training data necessary for successful training. In this contribution we investigate how input and target representations interplay with the amount of available training data in a music information retrieval setting. We compare the standard melspectrogram inputs with a newly proposed representation, called Mel scattering. Furthermore, we investigate the impact of additional target data representations by using an augmented target loss function which incorporates unused available information. We observe that all proposed methods outperform the standard meltransform representation when using a limited data set and discuss their strengths and limitations. The source code for reproducibility of our experiments as well as intermediate results and model checkpoints are available in an online repository.