Spatial Heterodyne Spectroscopy (SHS) is a hyperspectral analysis technique applied in weak matter detection, planetary exploration, and atmospheric remote sensing. Influenced by the complex experimental environment and the weak signal of the measured target, the measurement results of the Spatial Heterodyne Spectrograph are prone to tilted interference fringes and speckle noise in the interferograms, which ultimately affect the accuracy of the measured spectra. To solve these problems, this paper proposes a wavelet transform-based interferogram error analysis method, which effectively evaluates the interferogram's speckle noise level and stripe tilt error, thus providing a theoretical basis for the subsequent error correction. In this paper, Gaussian noise with different standard deviations is added to the error-free simulated interferograms of potassium lamps. The complex wavelet coefficients are extracted by using wavelet decomposition. Three noise estimation methods are used to compute the interferogram data. The results show that the noise estimation results of the spatial correlation wavelet transform method have the smallest deviation from the real value. The Donoho estimation method matches the real value better after the intercept correction. Subsequently, the Db2 wavelet decomposes the potassium lamp interferograms with different noise levels in one wavelet layer and extracts the detail coefficients in the horizontal, diagonal, and vertical directions. Donoho estimation is used to analyze the interferograms for two-dimensional noise analysis, which effectively characterizes the noise levels of the three interferograms in each direction. The research results show that the three directions of the wavelet detail coefficient valuation change respectively in the decomposition to different layers have a similar rule of change: the wavelet detail coefficient valuation and the stripe tilt direction, and the wavelet detail coefficient belongs to the direction of the angle is inversely proportional to the direction of the stripe tilt direction and the wavelet detail coefficient of the direction of the smaller the angle of the stripe tilt direction and the direction of the wavelet detail coefficient of the valuation of the larger, and vice versa, the smaller, and the horizontal direction of the first layer of the decomposition, the diagonal decomposition of the direction to the second layer of the vertical direction of the third layer of the hierarchy conforms to the rule of change. This study is a useful attempt to utilize wavelet decomposition for spatial outlier spectral error analysis and also provides a new way for subsequent correction of interferogram streak tilt error.