Long short-term memory (LSTM) has been effectively used to represent sequential data in recent years. However, LSTM still struggles with capturing the long-term temporal dependencies. In this paper, we propose an hourglass-shaped LSTM that is able to capture long-term temporal correlations by reducing the feature resolutions without data loss. We have used skip connections in non-adjacent layers to avoid gradient decay. In addition, an attention process is incorporated into skip connections to emphasize the essential spectral features and spectral regions. The proposed LSTM model is applied to speech enhancement and recognition applications. The proposed LSTM model uses no future information, resulting in a causal system suitable for real-time processing. The combined spectral feature sets are used to train the LSTM model for improved performance. Using the proposed model, the ideal ratio mask (IRM) is estimated as a training objective. The experimental evaluations using short-time objective intelligibility (STOI) and perceptual evaluation of speech quality (PESQ) have demonstrated that the proposed model with robust feature representation obtained higher speech intelligibility and perceptual quality. With the TIMIT, LibriSpeech, and VoiceBank datasets, the proposed model improved STOI by 16.21%, 16.41%, and 18.33% over noisy speech, whereas PESQ is improved by 31.1%, 32.9%, and 32%. In seen and unseen noisy situations, the proposed model outperformed existing deep neural networks (DNNs), including baseline LSTM, feedforward neural network (FDNN), convolutional neural network (CNN), and generative adversarial network (GAN). With the Kaldi toolkit for automated speech recognition (ASR), the proposed model significantly reduced the word error rates (WERs) and reached an average WER of 15.13% in noisy backgrounds.