Table 2 Solutions of the inequality model for single component/bi-component LFM signal added with zero-mean stationary noise

Solutions of the model

\(\frac{\left| b\left( h_1+1\right) \right| }{2}>1\)

\(\frac{\left| b\left( {\widehat{h}}_1+1\right) \right| +\left| b\left( {\widetilde{h}}_1+1\right) \right| }{4}>1\)

Constraints on parameters

\(2\beta b_1+a_1\ne 0\),

\(2{\widehat{\beta }}b_1+a_1\ne 0\), \(2{\widetilde{\beta }}b_1+a_1\ne 0\),

\(\frac{a}{2b}+\frac{d_1-h_1}{8b_1}-\frac{\beta }{4}=0\)

\(\frac{a}{2b}+\frac{d_1-{\widehat{h}}_1}{8b_1}-\frac{{\widehat{\beta }}}{4}=0\), \(\frac{a}{2b}+\frac{d_1-{\widetilde{h}}_1}{8b_1}-\frac{{\widetilde{\beta }}}{4}=0\)