# De-Noising Process in Room Impulse Response with Generalized Spectral Subtraction
## 1 Introduction  
Reverberation time (RT) is the most representative and physically important parameter related to the average properties of a room [1, 2, 3] and is essential for predicting speech intelligibility [4, 5]. A well-known and widely used method to calculate RT is determined by the energy decay curve (EDC) generated by [PERSON]'s method [6]; however, the measured room impulse response (RIR) presents ambient noise, and equipment noise may deteriorate the EDC, leading to errors in predicting room acoustic parameters [7, 8]. The relative errors for RTs, early decay time (EDT), and other acoustic parameters, without noise compensation, could exceed 5% [9, 10]. In the past few decades, studies and achievements have been based on using mathematical models to improve the accuracy of estimating RT, etc. To minimize the noise effects in the backward integration method, typical research focused on the noise compensation method to truncate the RIR at a point where the RIR decay intersects with the constant noise floor [7], which is technically the truncation time, to generate noise-free decay curves [11, 12]. Nevertheless, the performance of EDCs generated from different compensation methods is significantly influenced by the estimated upper integration time and the noise levels at the truncation time [13]. This problem identified two casual factors: the upper integration time of RIR and the estimated background noise levels at the truncation time. Consequently, a correction term was added to the integration to prevent the truncation error [9, 13, 14]. For mathematical advantages, nonlinear regression methods [15] were investigated to fit the RIR to calculate the slope of the EDC. The technique was further developed asan automated detection method for calculating the correction term and determining the truncation time [5; 8]. All the methods were set out from the time domain. Advanced technical methods have been applied to remove the non-decaying frequency-dependent noise floor of the direction room impulse response, measured with spherical microphone arrays with an exponentially decaying zero-mean Gaussian noise [16; 17]. An application of wavelet techniques for reducing the RT estimation error caused by noise showed the possibility of implementing the de-noising approach to reduce the noise of RIR [18]. Regarding well-known de-noising techniques involving a forward and an inverse Fourier transform [19] performed on the Frequency domain, spectral subtraction algorithms (SS) that have extraordinary ability in removing the signal noise levels were considered to minimize the noise effects on estimating acoustic parameters, such as RTs and EDT. The technique was used to de-noise the RIR because the algorithm has a similar de-noising rule to the noise subtraction method [20], in which the noise levels were subtracted from the noisy signal to estimate the clean signal. Unlike the SS algorithm, the de-noising processing of the noise subtraction method was conducted in the time domain. In contrast, the SS algorithms used a novel noise estimation approach to adaptively estimate the addictive noise levels during the silent periods of the signal and were subtracted from the noisy signals frame-by-frame. The methods were studied intensively based on short-time spectral amplitudes (STSA) and were used to suppress the noise with a relatively stable power spectral density. They were initially proposed for speech enhancement [21] and had been applied successfully in other areas, such as underwater acoustic sounds [22], speech dereverberation [23], and electronic noise reduction [24; 25]. Nevertheless, the random variations of noise leading to an inaccurate estimation of the noise levels and the processing of noise subtraction may result in much of the interfering noise remaining, causing some original signals to be removed [26]. Many algorithms have been developed to minimize the distortion caused by noise subtraction processing between an enhanced signal and a clean signal [27].